Non-homogenous differential Equation

  • Thread starter sndoyle1
  • Start date
  • #1
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Homework Statement


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


Homework Equations



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.
 

Answers and Replies

  • #2
798
1
Since it is in the form [itex]e^{ax}/x^k[/itex] try using [itex]Ae^{-3x}/x[/itex]
 
  • #3
6
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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.
 
  • #4
798
1
I usually always try the simplest first. This doesn't pertain to this question, but if [itex]Ae^{ax}[/itex] didn't work I would try [itex]Axe^{ax}[/itex], and if that didn't work I would try [itex]Ax^2e^{ax}[/itex]. It can be rather tedious for some questions but eventually you start to notice patterns.
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
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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".
 
  • #6
798
1
I think he accidentally hit the quotation mark key.
 

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