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Power series solution

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Compute the power series solution for the ODE y''+x^2y=0 and determine the radii of convergence for the two series solutions.

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Comparing the equation with the equation
, we get

does not vanish at .
Then is an ordinary point.

Let the solution in series form be



Putting the values of in (i), we get


This is an identity. Equating the coefficients of various powers of to zero, we get the following relations:





Solution Summary

This provides an example of power series solution and radii of convergence.