Find a general solution of the differential equation
xy'' − (1 + x2 )y' = 0.
Euler-Cauchy general form : xnyn+xn-1yn-1 ... +y=g(x)
The Attempt at a Solution
At first I tried using Euler-Cauchy but by multiplying by x (to get the x2 in front of y''), the term in front of y' becomes (x+x3) 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
Any ideas on how to solve this?