## Non-homogenous differential Equation

1. The problem statement, all variables and given/known data
solve:
y""+6y'+9y=e-3x/x3

2. Relevant equations

y=yc+yp

3. 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.

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 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.

## Non-homogenous differential Equation

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.

 Recognitions: Gold Member Science Advisor Staff Emeritus Is that really a fourth degree equation or is the second '' a typo? "Undetermined coefficents" works when the right side of the equation is one of the types of solutions you can get as solutions to homogenous differential equations with constant coefficients: exponentials, sine or cosine, and polynomials, as well as combinations of those. That is not the case here. I recommend "variation of parameters".
 I think he accidentally hit the quotation mark key.