# Singularity and Radius of Convergence

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4. Determine two independent power series solution of the differential equation:

See attachment for equation

Find the radius of convergence of the series.

5. Determine a solution of the differential equation:

See attachment for equation

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This solution shows how to solve problems related to singularity and convergence radius.

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Theorem:

Let x_0 be an ordinary point of the differential equation

L(y) = y'' + p(t)y' + q(t)y = 0

Then the general solution can be represented by the power series

where a_0 and ...

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