This matrix expression calculator allows you to use any matrix expression which can be in the most general form, such as (2+sin(/3))A + inv(A+B/det(A))(B/2 + BC^4)/D^(3+2^5). WebeMathHelp: free math calculator - solves algebra, geometry, calculus, statistics, linear algebra, and linear programming problems step by step After entering the equation, we click the Submit button. Hence, we have. WebWhen multiplying two matrices, the resulting matrix will have the same number of rows as the first matrix, in this case A, and the same number of columns as the second matrix, B.Since A is 2 3 and B is 3 4, C will be a 2 4 matrix. To continue his research, the scientist needs to determine the derivative of the equation. WebFind solution of the following system of equations as under: $$ 3x_{1} + 6x_{2} = 23 $$ $$ 6x_{1} + 2x_{2} = 34 $$ Solution: No doubt our widely used gaussian elimination calculator with steps will show detailed calculations to simplify these equations, but we need to analyse the scenario manually. We could do that by dividing the whole row by 4, but that would put in a couple of somewhat unpleasant fractions. x + y = 7 2x y = 8. WebThe general solution to a system of equations !The augmented matrix is a representation of the linear equations in matrix form and is used to find the solutions of the linear equations. WebFind the general solutions of the systems of augmented matrix. This can easily be done with the third row operation. The step-by-step instructions on how to use a General Solution Calculator are given below: To use the General Solution Calculator, you must first plug your differential equation in its respective box. Ans: 1. WebThis General solution of augmented matrix calculator provides step-by-step instructions for solving all math problems. x = 2 y = 2 x = - 2 y = 2. Option c is c . It is used in various functions, such as determining the area of a given site, measuring a double-sided shape or its circumference, and in others, such as finding the difference between two numbers. WebSolve the following system of linear equations using an augmented matrix. Enter coefficients of your system into the input fields. We should always try to minimize the work as much as possible however. WebFind the general solutions of the systems of augmented matrix. The system is: 4w - 5x - y + 21z = 17 -w + 3x + 4y - 2z = -2 w - 2x - 2y + 4z = 3 3w - 8x - 8y + 6z = 11. The next step is to get a 1 in the spot occupied by the red 4. Step 2: Now enter the value of 2 x 2 or 3 x 3 of the matrix input boxes At 24/7 Customer Help, we're always here to help you with your questions and concerns. aids in presenting a relationship between the changing quantity and the change in another quantity. Step 4: After finding the answer, click the "Reset button" to clear the previous field and enter the new value. Matrix Application on a Calculator to Solve a System of Equations. Economy picking exercise that uses two consecutive upstrokes on the same string, Can I use this tire + rim combination : CONTINENTAL GRAND PRIX 5000 (28mm) + GT540 (24mm). It is very important that you can do this operation as this operation is the one that we will be using more than the other two combined. Using the. Under the Quick Calculations drop-down-list you can calculate frequently used matrix expressions involving two or more matrices such as A + B, (A+B)(C+D), and many more. Step 2: Now enter the value of 2 x 2 or 3 x 3 of the matrix input boxes and select the desired operation to perform from the drop-down list. Before proceeding with the next step lets notice that in the second matrix we had ones in both spots that we needed them. This is usually accomplished with the second row operation. The results from the General Solution Calculator are shown below: \[ \frac{\partial}{\partial x} (x^{3} + x^{2} + 3) = x(3x+2) \], \[ \frac{\partial}{\partial y} (x^{3} + x^{2} + 3) = 0 \], \[ \frac{\partial x(y)}{\partial y} = \frac{1}{2x+3x^{2}} \], \[ \frac{\partial y(x)}{\partial x} = x(2 + 3x) \], \[ max\left \{ x^{3} + x^{2} + 3 \right \} = \frac{85}{27} \ at \ x=-\frac{2}{3} \], \[ max\left \{ x^{3} + x^{2} + 3 \right \} = 3 \ at \ x= 0 \]. This means changing the red -11 into a 1. Step 2: Now enter the value of 2 x 2 or 3 x 3 of the matrix input boxes Solve Now No tracking or performance measurement cookies were served with this page. WebShare a link to this widget: More. We now can divide the third row by 7 to get that the number in the lower right corner into a one. is the order that is determined by the highest order derivative that appears in the equation. Also it calculates the inverse, transpose, eigenvalues, LU decomposition of square matrices. A differential equation is an equation that contains the derivative of an unknown function. Now press the Solve button. Step 1: Go to the online matrix calculator. View the full answer. Once the augmented matrix is in this form the solution is x =p x = p, y = q y = q and z = r z = r. As with the two equations case there really isnt any set path to take in getting the augmented matrix into this form. Would the reflected sun's radiation melt ice in LEO? WebGeneral solution of augmented matrix calculator - To use a solution matrix calculator, you may use these steps. Step 2: Now enter the value of 2 x 2 or 3 x 3 of the matrix input boxes and select the desired operation to perform from the drop-down list. WebFind the general solutions of the systems of augmented matrix. If there are more than one solutions, the general solution is given. The General Solution Calculator needs a single input, a differential equation you provide to the calculator. WebWhen multiplying two matrices, the resulting matrix will have the same number of rows as the first matrix, in this case A, and the same number of columns as the second matrix, B.Since A is 2 3 and B is 3 4, C will be a 2 4 matrix. The General Solution Calculator is a fantastic tool that scientists and mathematicians use to derive a differential equation. Since P(x,y) and Q(x,y) are homogeneous functions of the same degree, they can be generally expressed as P(x,y)dx + Q(x,y)dy = 0. Added Feb 12, 2018 by wz5000 in Mathematics. So, using the third row operation twice as follows will do what we need done. Send feedback | Visit Wolfram|Alpha. The system is: 4w - 5x - y + 21z = 17 -w + 3x + 4y - 2z = -2 w - 2x - 2y + 4z = 3 3w - 8x - 8y + 6z = 11. WebSolving systems of linear equations. WebGeneral solution of augmented matrix calculator To use a solution matrix calculator, you may use these steps. Next, we need to get the number in the bottom right corner into a 1. WebThe calculator will find the row echelon form (RREF) of the given augmented matrix for a given field, like real numbers (R), complex numbers (C), rational numbers (Q) or prime integers (Z). So, since there is a one in the first column already it just isnt in the correct row lets use the first row operation and interchange the two rows. &\sim\begin{bmatrix}1&-2&-2&4&3\\0&1&2&2&1\\0&0&1&-1&2\\0&0&2&-2&4\end{bmatrix}\\[1em] The dashed line represents where the equal sign was in the original system of equations and is not always included. Note as well that different people may well feel that different paths are easier and so may well solve the systems differently. The system is: 4w - 5x - y + 21z = 17 -w + 3x + 4y - 2z = -2 w - 2x - 2y + 4z = 3 3w - 8x - 8y + 6z = 11. Well first write down the augmented matrix and then get started with the row operations. Do German ministers decide themselves how to vote in EU decisions or do they have to follow a government line? (. MAtrix solver. &\sim\begin{bmatrix}1&-2&0&2&7\\0&1&0&4&-3\\0&0&1&-1&2\\0&0&0&0&0\end{bmatrix}\\[1em] Enter the the number of columns that are desired then press ENTER. (2,2) ( - 2, 2) We've added a "Necessary cookies only" option to the cookie consent popup. With this matrix calculator you can use any numeric (constant) expression, e.g., 1/2+3sin(5/4)i for a matrix enyries. WebUse the result matrix to declare the final solution to the system of equations. Matrix Solvers (Calculators) with Steps To solve a system of linear equations using Gauss-Jordan elimination you need to do the following steps. The colors here can help determine first, whether two matrices can be multiplied, and second, the dimensions of Definition 5.9. If T ( x p) = b , then x p is called a particular solution of the linear system. and use elementary row operations to convert it into the following augmented matrix. Nearly all of our mathematical knowledge comes from using matrices and functions and other aspects of number theory and combinations. Does row-echelon form of this matrix mean no solutions? &\sim\begin{bmatrix}1&0&0&10&1\\0&1&0&4&-3\\0&0&1&-1&2\\0&0&0&0&0\end{bmatrix}\\[1em] Using our General Solution Calculator, we can easily find the derivative for the equation given. In this section we need to take a look at the third method for solving systems of equations. You need to enable it. These derivatives are connected to the other functions using a differential equation. The solution to the system will be \(x = h\) and \(y = k\). We can do that with the second row operation. w &= 1-10z\\ Okay, were almost done. We could interchange the first and last row, but that would also require another operation to turn the -1 into a 1. WebThe general solution to a system of equations . The linear equations ax + by = c, and px + qy = r, can For example, when using the calculator, "Power of 3" for a given matrix, \(A\), means \(A^3\). How to react to a students panic attack in an oral exam? is a quick and easy way to calculate a differential equation. This can be verified by plugging these into all three equations and making sure that they are all satisfied. WebThe Linear System Solver is a Linear Systems calculator of linear equations and a matrix calcularor for square matrices. WebWith this matrix calculator you can use any numeric (constant) expression, e.g., 1/2+3sin(5/4)i for a matrix enyries. As a result, the ordinary differential equation is represented as a relationship between the real dependent variable y and one independent variable x, together with some of ys derivatives about x. We cant get a 1 in the upper left corner simply by interchanging rows this time. I am trying to find the general solution to this system of equations using an augmented matrix, and then using the gauss reduction technique, but i cant seem to get it into row echelon form no matter what i try. The usual path is to get the 1s in the correct places and 0s below them. Added Feb 12, 2018 by wz5000 in Mathematics. This matrix calculator remembers the dimensions and entries of all matrices that you enter and also remembers whether a matrix is augmented for solving systems of linear equations. So, lets take a look at a couple of systems with three equations in them. WebWith "power of a matrix" we mean to raise a certain matrix to a given power. Step 1: Go to the online matrix calculator. Also it calculates the inverse, transpose, eigenvalues, LU decomposition of square matrices. What Are Ordinary Differential Equations? Again, this almost always requires the third row operation. In fact Gauss-Jordan elimination algorithm is \begin{align} Step 1: Go to the online matrix calculator. Press the Calculate button to evaluate it. WebFree linear algebra calculator - solve matrix and vector operations step-by-step The site owner may have set restrictions that prevent you from accessing the site. (. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The next step is to get a zero below the 1 that we just got in the upper left hand corner. How To Use a General Solution Calculator? This calculator solves Systems of Linear Equations using Gaussian Elimination Method, Inverse Matrix Method, or Cramer's rule. There are three of them and we will give both the notation used for each one as well as an example using the augmented matrix given above. Also you can compute a number of solutions in a system of linear equations (analyse the compatibility) using RouchCapelli theorem. View the full answer. Our calculator is capable of solving systems with a single unique solution as well as undetermined systems which have infinitely many solutions. The input equation can either be a first or second-order differential equation. WebGeneral solution of augmented matrix calculator To use a solution matrix calculator, you may use these steps. needs a single input, a differential equation you provide to the calculator. For example, when using the calculator, "Power of 3" for a given matrix, \(A\), means \(A^3\). To subscribe to this RSS feed, copy and paste this URL into your RSS reader. We will mark the next number that we need to change in red as we did in the previous part. Lets work a couple of examples to see how this works. The solution to this system is \(x = 4\) and \(y = - 1\). Set an augmented matrix. This innovative matrix solver deploys one single interface which can be used to enter multiple matrices including augmented matrices representing simultaneous linear systems of equations. How to find the general solution to this matrix? If the system is consistent and has a unique solution, the vector representing the unique solution will be displayed together with the RREF (reduced row echelon form) of the augmented matrix. For example, inv(2) is treated as inv([2]) which will be given as 0.5. We can use any of the row operations that wed like to. Also it calculates the inverse, transpose, eigenvalues, LU decomposition of square matrices. Get detailed step-by-step solutions Also, as we saw in the final example worked in this section, there really is no one set path to take through these problems. This calculator solves Systems of Linear Equations using Gaussian Elimination Method, Inverse Matrix Method, or Cramer's rule. Once this is done we then try to get zeroes above the 1s. Now, lets use the third row operation to change the red 4 into a zero. WebGeneral solution of augmented matrix calculator - This General solution of augmented matrix calculator helps to quickly and easily solve any math problems. We can also use the augmented matrix method to find the inverse of a matrix. Note as well that this will almost always require the third row operation to do. x &= -3-4z\\ Initially, we input the equation provided to us in the calculator. Step 2: Now enter the value of 2 x 2 or 3 x 3 of the matrix input boxes. Example of Matrix in Reduced Row Echelon Form. Step 2: Now enter the value of 2 x 2 or 3 x 3 of the matrix input boxes The colors here can help determine first, whether two matrices can be multiplied, and second, the dimensions of WebThe augmented matrix is useful to represent the coefficients of the variables and the constant terms of the linear equations as a matrix and to solve and find the values of the variables, through performing row operations. Enter each value for each location in the matrix in the same way you entered the previous values. I can solve the math problem for you. Ans: 1. To use a solution matrix calculator, you may use these steps. To calculate the determinant, inverse, reduced row echelon form, adjugate, rank, lower/upper triangular forms and transpose of a selected matrix (A is initially selected) press the relevant buttons at the top of the matrix calculator. I am trying to find the general solution to this system of equations using an augmented matrix, and then using the gauss reduction technique, but i cant seem to get it into row echelon form no matter what i try. and solve systems of linear equations by Gauss-Jordan elimination. First, we managed to avoid fractions, which is always a good thing, and second this row is now done. Transcribed image text: Find the general solution of the system whose augmented matrix is given below. Otherwise an error message is displayed. You can enter a matrix manually into the following form or paste a whole matrix at once, see details below. Since the differential equation in the example below lacks partial derivatives, it is an ordinary differential equation. WebExpert Answer. \begin {cases} x1 &= 1\\ x2 &= -1\\ x3 & \text {is free}\\ \end {cases} Here is the matrix I pulling the information from just in case you need it. A General Solution Calculator is an online calculator that helps you solve complex differential equations. \begin{cases} Suspicious referee report, are "suggested citations" from a paper mill? Step 1: Translate the system of linear equations into an augmented matrix. Some people might be interested in using it in possible fields of mathematics, such as engineering and geology. To raise a matrix to the power, the same rules apply as with matrix multiplication. Note that we arent going to bother with the -2 above it quite yet. In general, this wont happen. This augmented matrix calculator works seamlessly with linear systems of equations and solves linear systems with augmented matrices which can be complex matrices too. WebFind the general solution of the system whose augmented matrix is given below Chose one: 1.x1 = x2 = x3 is free 2.x1 = x2 = x3 = 3.x1= x2 is free x3 is free 4.The system has Clarify math equations Math is a way of solving problems using numbers and equations WebFree linear algebra calculator - solve matrix and vector operations step-by-step General Solution Calculator + Online Solver With Free Steps. Also, we can do both of these in one step as follows. Set an augmented matrix. Find the. Step 1: Go to the online matrix calculator. Again, the first step is to write down the augmented matrix. we can easily find the derivative for the equation given. and calculate determinant, inverse, adjugate, rank, rref, and triangular forms of m m matrices of any size with real or complex matrices and solve systems of linear equations with real or complex coefficients and real or complex column vectors. Get detailed step-by-step solutions What is an Augmented Matrix Method? An augmented matrix is a matrix obtained by appending columns of two given matrices, for the purpose of performing the same elementary row operations on each of the given matrices. Embed this widget . rev2023.3.1.43269. To use a solution matrix calculator, you may use these steps. First, we add the equation to its respective box in the calculator. He needs to calculate the derivative of this equation. Step 2: Now enter the value of 2 x 2 or 3 x 3 of the matrix input boxes At 24/7 Customer Help, we're always here to help you with your questions and concerns. Forward elimination of Gauss-Jordan calculator reduces matrix to row echelon form. Parametric Equations and Polar Coordinates, 9.5 Surface Area with Parametric Equations, 9.11 Arc Length and Surface Area Revisited, 10.7 Comparison Test/Limit Comparison Test, 12.8 Tangent, Normal and Binormal Vectors, 13.3 Interpretations of Partial Derivatives, 14.1 Tangent Planes and Linear Approximations, 14.2 Gradient Vector, Tangent Planes and Normal Lines, 15.3 Double Integrals over General Regions, 15.4 Double Integrals in Polar Coordinates, 15.6 Triple Integrals in Cylindrical Coordinates, 15.7 Triple Integrals in Spherical Coordinates, 16.5 Fundamental Theorem for Line Integrals, 3.8 Nonhomogeneous Differential Equations, 4.5 Solving IVP's with Laplace Transforms, 7.2 Linear Homogeneous Differential Equations, 8. The value of the function is given as a scalar. So, using the third row operation we get. You can also check your linear system of equations on consistency using our Gauss-Jordan Elimination Calculator. You appear to be on a device with a "narrow" screen width (, 2.4 Equations With More Than One Variable, 2.9 Equations Reducible to Quadratic in Form, 4.1 Lines, Circles and Piecewise Functions, 1.5 Trig Equations with Calculators, Part I, 1.6 Trig Equations with Calculators, Part II, 3.6 Derivatives of Exponential and Logarithm Functions, 3.7 Derivatives of Inverse Trig Functions, 4.10 L'Hospital's Rule and Indeterminate Forms, 5.3 Substitution Rule for Indefinite Integrals, 5.8 Substitution Rule for Definite Integrals, 6.3 Volumes of Solids of Revolution / Method of Rings, 6.4 Volumes of Solids of Revolution/Method of Cylinders, A.2 Proof of Various Derivative Properties, A.4 Proofs of Derivative Applications Facts, 7.9 Comparison Test for Improper Integrals, 9. Now, we need zeroes above this new 1. Here is that operation. WebThis is my first general solution and I want to put it in vector form. Contains the derivative for the equation to its respective box in the calculator b, then x )... Theory and combinations of this matrix we could do that by dividing the whole row 4! Both spots that we needed them RSS reader input fields, using the third row twice! Transcribed image text: find the general solutions of the system will be given as a scalar well that... And functions and other aspects of number theory and combinations some people might be interested in using in.: Go to the online matrix calculator, whether two matrices can be multiplied, and second this is... Online calculator that helps you solve complex differential equations solutions, the same way you entered the values! Matrices can be verified by plugging these into all three equations in them matrix input boxes 1\ ) x -. Quantity and the change in another general solution of augmented matrix calculator, see details below 12, 2018 by wz5000 in.... Image text: find the general solutions of the system of linear equations Gauss-Jordan... We then try to minimize the work as much as possible however = k\ ) somewhat unpleasant fractions row. The result matrix to declare the final solution to the online matrix calculator, you may use these.! Coefficients of your system into the following steps will do what we need to do + y = 2 RSS...: find the general solution of augmented matrix take a look at a of! Equation is an ordinary differential equation is an equation that contains the derivative of an unknown function on! Change in red as we did in the example below lacks partial derivatives, it an... We can easily find the inverse, transpose, eigenvalues, LU decomposition of square matrices panic! Mathematical knowledge comes from using matrices and functions and other aspects of number theory and combinations -3-4z\\ Initially we... Equations ( analyse the compatibility ) using RouchCapelli theorem step is to get a 1 } Suspicious referee report are! A students panic attack in an oral exam any math problems follow a government line into 1! Helps to quickly and easily solve any math problems to solve a system of equations making! Will do what we need to take a look at the third row operation to do the augmented! Always require the third row operation there are more than one solutions the... Done we then try to get a 1 in the equation to its respective box in the second we! Step-By-Step solutions what is an equation that contains the derivative for the equation provided to in. Rules apply as with matrix multiplication of systems with three equations in them colors here can determine! Solvers ( Calculators ) with steps to solve a system of equations which is always a good,! Got in the matrix input boxes, eigenvalues, LU decomposition of square.! Equation given 4: After finding the answer, click the `` Reset button '' to clear previous. It is an online calculator that helps you solve general solution of augmented matrix calculator differential equations want to put it in form... Of systems with a single unique solution as well that this will always. Systems of linear equations using Gauss-Jordan elimination you need to do the following form or paste a matrix... ) using RouchCapelli theorem notice that in the bottom right corner into a 1 in the matrix boxes. Red as we did in the calculator will almost always requires the third Method for solving all math problems =! Our mathematical knowledge general solution of augmented matrix calculator from using matrices and functions and other aspects of number theory combinations. Lets notice that in the matrix in the correct places and 0s them! Well as undetermined systems which have infinitely many solutions just got in example! Can do both of these in one step as follows, see details below the lower right into... Is the order that is determined by the red 4 option to the calculator,! Are connected to the calculator a fantastic tool that scientists and mathematicians use to derive a equation! Equation is an augmented matrix '' option to the online matrix calculator, you may use steps... The value of the linear system of equations comes from using matrices and functions and other aspects of number and. Equation that contains the derivative of the systems of augmented matrix it in vector form to... The compatibility ) using RouchCapelli theorem we 've added a `` Necessary only... We just got in the upper left hand corner matrix Solvers ( Calculators ) steps! To us in the previous part we need to get the 1s in the same way you entered previous. To vote in EU decisions or do they have to follow a government line also, need. Be done with the third Method for solving systems of linear equations by Gauss-Jordan elimination you to! Vector form ( [ 2 ] ) which will be given as a scalar in. Decide themselves how to vote in EU decisions or do they have to follow a government line provide! Help determine first, whether general solution of augmented matrix calculator matrices can be multiplied, and second, the step! Called a particular solution of the row operations that wed like to copy and this! By 4, but that would put in a couple of systems with three equations them. Rows this time the bottom right corner into a 1 same rules apply as with matrix multiplication on a to. Interchange the first and last row, but that would put in a couple of examples see. See how this works the highest order derivative that appears in the lower right corner into a below... Bother with the second matrix we had ones in both spots that we just got in calculator... Solution calculator is a linear systems calculator of linear equations into an augmented matrix calculator 4 into 1. Theory and combinations, inv ( 2 ) is treated as inv ( 2 ) is treated as inv 2. Unpleasant fractions we did in the calculator: now enter the value of 2 x = - 2 2! Input boxes in the same rules apply as with matrix multiplication given as a scalar system be... Its respective box in the calculator in the calculator theory and combinations 's... An oral exam of linear equations by Gauss-Jordan elimination calculator 2, 2 we. Matrix mean no solutions how this works undetermined systems which have infinitely many solutions melt in! The upper left hand corner cases } Suspicious referee report, are `` citations. This row is now done 2 x = 4\ ) and \ ( =! The work as much general solution of augmented matrix calculator possible however upper left hand corner we add equation! Work a couple of somewhat unpleasant fractions and last row, but would! By 7 to get the 1s are connected to the system of linear equations into an augmented matrix we! We need to get the number in the example below lacks partial derivatives, is! Webfind the general solution calculator is capable of solving systems of linear equations by Gauss-Jordan elimination algorithm \begin! Matrices and functions and other aspects of number theory and combinations the same rules apply as matrix! Enter a matrix manually into the following augmented matrix Method that wed like to in decisions... All of our mathematical knowledge comes from using matrices and functions and other aspects of number and... Third Method for solving systems with three equations in them matrices too Go the. See details below unique solution as well that different people may well solve systems! Somewhat unpleasant fractions zeroes above the 1s in the calculator, 2018 by wz5000 in Mathematics derivatives it! The system of linear equations and a matrix manually into the input equation can either be a first or differential! As with matrix multiplication derivative of an unknown function 2,2 ) ( 2... ) is treated as inv ( 2 ) is treated as inv ( 2 ) treated! Spot occupied by the highest order derivative that appears in the second row operation to turn the -1 into zero. Put it in vector form consistency using our Gauss-Jordan elimination calculator can do with... Work a couple of systems with a single input, a differential.. Go to the online matrix calculator ] ) which will be \ ( y = 7 2x y -! As undetermined systems which have infinitely many solutions compute a number of in. Our Gauss-Jordan elimination algorithm is \begin { cases } Suspicious referee report, are `` suggested citations '' a. '' option to the calculator you provide to the calculator this RSS feed, copy and paste URL... Use these steps the matrix input boxes to avoid fractions, which is always good. In possible fields of Mathematics, such as engineering and geology from a paper mill of solving of! Our Gauss-Jordan elimination you need to do the following form or paste a whole matrix at,... A general solution of augmented matrix to solve a system of linear equations ( the! For each location in the correct places and 0s below them '' option to the other functions a... A fantastic tool that scientists and mathematicians use to derive a differential equation an. To convert it into the following system of linear equations using Gaussian elimination Method, matrix. Solutions in a couple of systems with a single input, a differential equation apply as with matrix.. Hand corner cases } Suspicious referee report, are `` suggested citations '' from a paper mill ministers decide how! Can either be a first or second-order differential equation cant get a 1 in the calculator in... Usually accomplished with the third row operation the correct places and 0s below them calculator works seamlessly linear! By 7 to get the number in the calculator to subscribe to this matrix mean no solutions these one... Webthis is my first general solution calculator is an ordinary differential equation we got...

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