# Thread: Second Order inhomogeneous O.D.E: Particular Integral when f(x)=x^k (k<0)

1. ## Second Order inhomogeneous O.D.E: Particular Integral when f(x)=x^k (k<0)

Hey guys,

What form of approximations of particular integral do I choose when the forcing f(x) is a polynomial of a negative order?

Here is my O.D.E which I'm solving:

I've made a Euler variable substitution of t=lnx which has removed the non-constant coefficients. This gives:

$\ddot{y}+3\dot{y}+2y=\frac{3}{t^{2}}$

Normally for a polynomial of degree n where n>0, I'd just try a generic polynomial of degree n with all terms down to the integer.

Any ideas folks?

Edit: Stupid mistake with the variable substitution. Nothing to see here!