Symbolic solution of differential equations
Symbolic treatment of a few types of differential equations is coded in the SciPy stack through the module sympy.solvers.ode. At this point, only the following equations are accessible with this method:
- First order separable
- First order homogeneous
- First order exact
- First order linear
- First order Bernoulli
- Second order Liouville
- Any order linear equations with constant coefficients
In addition to these, other equations might be solvable with the following techniques:
- A power series solution for the first or second order equations (the latter only at ordinary and regular singular points)
- The lie group method for the first order equations
Let's see these techniques in action with our one-dimensional examples, y' = y and the Bernoulli equation. Note the method of inputting a differential equation. We write it in the form F(t,y,y') = 0, and we feed the expression F(t,y,y') to the solver (see line 3 that follows). Also, notice how we code...
