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## Homework Statement

(Reduction of order) The function y

_{1}= x

^{-1/2}cosx is one solution to the differential equation x

^{2}y" + xy' + (x

^{2}- 1/4) = 0. Use the method of reduction of order to find another linearly independent solution.

## The Attempt at a Solution

I divided x

^{2}to both sides to get the equation into y" + py' + qy = 0

y" + (1/x)y' + ((1 - (1/4x

^{2})) = 0

Using Abel's method

c e

^{-∫(p)dx}

= c e

^{-ln x}y

_{2}= -c lnx[/B]

Am I doing this right?