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Nonhomogenous differential Equation 
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#1
Feb2713, 07:27 PM

P: 6

1. The problem statement, all variables and given/known data
solve: y""+6y'+9y=e^{3x}/x^{3} 2. Relevant equations y=y_{c}+y_{p} 3. The attempt at a solution I found y_{c}=C_{1}e^{3x}+C_{2}xe^{3x} and am having difficulties finding yp. I am wondering which method would be the best to determine y_{p}:  annihilators  undetermined coefficients  variation of paramaters. 


#2
Feb2713, 07:55 PM

P: 778

Since it is in the form [itex]e^{ax}/x^k[/itex] try using [itex]Ae^{3x}/x[/itex]



#3
Feb2713, 09:09 PM

P: 6

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
Feb2713, 09:37 PM

P: 778

Nonhomogenous differential Equation
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
Feb2813, 08:13 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,558

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
Feb2813, 12:12 PM

P: 778

I think he accidentally hit the quotation mark key.



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