This is a symbolic solver for linear ordinary differential equations of order 2 written for the free computer algebra system Maxima. In order to use it put the file ode2singular.mac in one of the paths that is in your file_search_maxima variable and enter load('ode2singular); in Maxima. The file ode2singular.wxmx to be used with wxMaxima contains some examples of equations that can be solved by ode2singular. The file singular_points.pdf contains some explanations on the algorithm.
The function ode2singular tries to determine the singular points of the equation and use this information to solve it. If it doesn't succeed, the user can propose a change of variable and ode2singular tries to solve the equation with the new variable.
Examples of usage:
- In order to solve the equation
x^2 * y''(x) + x * y'(x) + y(x) = 0
enter in Maxima:
eq: x^2 * 'diff(y,x,2) + x * 'diff(y,x) + y = 0;
ode2singular(eq, y, x);
- In order to solve Mathieu's equation with a change of variable replacing x by cos(x) enter:
eq: 'diff(y,x,2) + (a-2*q*cos(2*x)) * y = 0;
phi: cos(x);
phi_inv: acos(x);
ode2singular_transform(eq, y, x, phi, phi_inv);