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## Homework Statement

Find a general solution of the differential equation

xy'' − (1 + x

^{2})y' = 0.

## Homework Equations

Euler-Cauchy general form : x

^{n}y

^{n}+x

^{n-1}y

^{n-1}... +y=g(x)

## The Attempt at a Solution

At first I tried using Euler-Cauchy but by multiplying by x (to get the x

^{2}in front of y''), the term in front of y' becomes (x+x

^{3}) and I don't know how to deal with that. I looked in my book and could not find any similar example.

I tried with power series but no luck, and since they are not in the midterm it means we have to use some other method to solve this problem.

According to wolframalpha the answer is supposed to be y(x) = c_1 e^(x^2/2)+c_2

http://www.wolframalpha.com/input/?i=x*y''-(1%2Bx^2)y'%3D0

Any ideas on how to solve this?