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 derivatives of a function...