How do I find a series solution to an ODE? I do not mean taking the Taylor series of an exact solution; I want to solve nasty nonlinear differential equations locally via plug and chug. Surely, that is a built-in option in Mathematica.
This method of developing a truncated solution can be done as below. I illustrate with an example that DSolve does not seem much to like.
We create a differentail operator to create this ode.
Now set up our Taylor series as a symbolic expansion using derivatives of
Next apply the differential operator and add the initial conditions. Then find a solution that makes all powers of `t vanish.
Let's look at the Taylor polynomial.
To assess how accurate it might be I will compare with
J.M. in a comment above alluded to this possibility. Using