Solving y'' + 2xy' + (1+x2)y = 0

[zorro]

I have a trouble finding a method other than Variation of Parameters to solve
y'' + 2xy' + (1+x²)y = 0.

Does there exist any other method?

 

[HallsofIvy]

I am confused as to what you mean by using "variation of parameters" to solve this. I was under the impression that variation of parameters was a method for finding a particular solution to a non-homogeneous equation after you had found the general solution to the related homogeneous equation.

For a linear equation with variable coefficients, like that, a series solution is the standard method.