Power series solution for differential equations. Is the solution to differential equations using power series applicable only to homogeneous differential equations?

ezelsbankuk

ezelsbankuk

Answered question

2022-09-09

Power series solution for differential equations
Is the solution to differential equations using power series applicable only to homogeneous differential equations? I mean equations of the form:
a 2 ϕ ( x ) + a 1 ϕ ( x ) + ϕ ( x ) = 0

Answer & Explanation

Kendall Ponce

Kendall Ponce

Beginner2022-09-10Added 18 answers

Step 1
If you have a source term f that admits a power series decomposition, you can apply the power series method to find a solution of your equation.
Also, this method can be extended to differential equations of any degrees. It also works if your coefficient a i are in the form a i x k for any k.
Step 2
Finaly, I would add that you need to be careful with this method if you have a non-linear O.D.E.

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