Solve this differential equation by using power series
y''-x^2y=o

We're looking for a solution

which has second derivative

Substituting these into the ODE gives

Right away we see , and the coefficients are given according to the recurrence

There's a dependency between terms in the sequence that are 4 indices apart, so we consider 4 different cases.

and so on, with the general pattern

and so on, with

Then the solution to this ODE is

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step-by-step explanation: