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## Homework Statement

Please help me with this, I would really appreciate it:

Using the fact that y1 = x

^{-1/2}cos x is a solution of the associated homogeneous problem, obtain the general solution of

x

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

^{2}- 1/4)y = x

^{3/2}

## The Attempt at a Solution

Well the first thing i did was divide it by x^2 to obtain:

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

^{2})y = x

^{-1/2}

Then let y'' + 1/x y' + (1 - 1/4x

^{2})y = 0

A second solution will be given as

y2 = y1 [tex]\int e ^ \int P(x)\frac{}{} (y1)^2[/tex] e

^{integral of P(x) dx}[tex]\div[/tex] (y1)^2

So here is where i have a problem, can someone please help me integrate

y2 = x

^{-1/2}cos x [tex]\int[/tex] - x / ( x

^{-1/2}cos x)^2

please help me..?