# Non-homogenous differential Equation

## Homework Statement

solve:
y""+6y'+9y=e-3x/x3

y=yc+yp

## The Attempt at a Solution

I found yc=C1e-3x+C2xe-3x
and am having difficulties finding yp. I am wondering which method would be the best to determine yp:

- annihilators
- undetermined coefficients
- variation of paramaters.

Since it is in the form $e^{ax}/x^k$ try using $Ae^{-3x}/x$

Thanks, it worked out. I have a hard time knowing what 'guess' to use for the derivative. How did you know to put it over x instead of x-3? I have a test tomorrow, so I want to make sure that I can do things properly.

I usually always try the simplest first. This doesn't pertain to this question, but if $Ae^{ax}$ didn't work I would try $Axe^{ax}$, and if that didn't work I would try $Ax^2e^{ax}$. It can be rather tedious for some questions but eventually you start to notice patterns.

HallsofIvy