Integral of exponential over polynomial

[AAO]

Homework Statement

Solve the ODE: y''+x*y'-y=0

Homework Equations

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 anyone tell me how to approach this integral:

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

 

[Samy_A]

Homework Statement

Solve the ODE: y''+x*y'-y=0

Homework Equations

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 anyone tell me how to approach this integral:

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

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