The present work aims to create a program to solve Ordinary differential equations of the second order. Using MathWorks compiler — where the sympy library is already imported, sympy was just imported as sp. Additionally, from sympy * (all) was imported.
1. First, defining y as a function of x: syms y(x)
Then, defining the coefficients of y'', y' and y as input functions
coff1 = input("cofficcient 1: ");
coff2 = input("cofficcient 2: ");
coff3 = input("cofficcient 3: ");
- Secondly, initializing f(x) fx= input("f(X): "); 3. Third step is to define the second order general form of ordinary differential equation The first coefficient is multiplied with the second derivative of y (y'') with respect to x. The second coefficient is multiplied by the first derivative of y (y’) The third coefficient is multiplied by y, and the function of x f(x).
Using the desolve function from the sympy library solve the ode for y
After period of coding, it is time to test plan. The testing is considering the problem sets that were associated — by professors of EJUST University — in Ordinary differential equation course.
| Methodology | Question |
|---|---|
| Substituting the coefficients of question number 1 | y′′ + 4y = 0 |
| Substituting the coefficients of question number 5 | 4y′′ − 4y + y = 0 |
| Substituting the coefficients of question number 7 | y′′ + 3y′ + 2y = 6 |
| Substituting the coefficients of question number 14 | y′′ − 6y′ + 9y = e^3x/x^2 |
| Substituting the coefficients of question number 20 | x^2 y′′− 3xy′ + 3y = 2x^4 |
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Mathematics is a science until the stage of vision, then it is turned into magical fiction. Accordingly, we decided to illustrate a visualization for our second ordinary differential equation by plotting the data into a graph as shown by function ezplot(ySol).
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