Integral of exponential over polynomial

1. Jan 5, 2016

AAO

1. The problem statement, all variables and given/known data
Solve the ODE: y''+x*y'-y=0

2. Relevant equations

3. The attempt at a solution
Since this is a variable coefficient ODE, I have used the method of reduction of order, and assumed the solution in the form: y=c1*y1+c2*y2

In this case: y1=x, and I have the reached the integral below for the second solution (y2), Can any one tell me how to approach this integral:

v=integral[ (x^-2) * exp (-0.5*x^2) dx]

Last edited by a moderator: Jan 5, 2016
2. Jan 5, 2016

Samy_A

Integration by parts leaves you with an integral that is (up to some constants) the error function.

Last edited by a moderator: Jan 5, 2016