How to solve differential equation series solution

How can I solve differential equation series in general solution in sage? Also, how can I adjust the default center x0=0 to another value(for example, x0=2)?

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Try :

desolve?


then

desolve_system?


This should go a long way towards solving your problem.

BTW, you should try the universal algorithm (a. k. a. RTFM)...

Googling sagemath documentation leads you there, where you'll find, among many other things, links to various tutorials.

( 2023-03-09 19:25:15 +0200 )edit

My advice is to search for:

solve_linear_de in https://doc.sagemath.org/html/en/refe...

1st_power_series

2nd_power_series_ordinary

2nd_power_series_regular in https://docs.sympy.org/latest/modules...

In Sympy if the initial data are given at x0=1, then the expansion is around 1

The default center x0=0 can be adjusted in https://fricas.github.io/book.pdf p.353.

In some cases the initial conditions may be symbolic, so general solutions can be obtained

( 2023-03-10 17:37:45 +0200 )edit