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Differential Equations 84 Online
OpenStudy (anonymous):

I'm having trouble with a couple of nonhomogenous initial value problems. i need to use the method of undetermined coefficients. I believe the problem lies in my guess when trying to solve the particular. any help would be greatly appreciated. here are the problems y''-2'+y = te^t+4, y'(0)=1,y(0)=1 or y''+4y=3sin(2t), y'(0)=-1, y(0)=2

OpenStudy (tkhunny):

Solve: \(r^{2} - 2r + 1 = 0\)

OpenStudy (anonymous):

I've done that. r=1. now i need to solve the particular but my initial guesses keep canceling out.

OpenStudy (tkhunny):

What did you use for potential solution functions?

OpenStudy (anonymous):

e^t(At+B)

OpenStudy (anonymous):

\[ \Large (At+C)e^t+D \] Is what I would try for a first guess, but keep in mind that e^t is already a solution, in fact it's a double root

OpenStudy (anonymous):

So this needs some manipulation still, to work out.

OpenStudy (tkhunny):

Keep adding ts We have two identical positive, Real roots. This suggests \(Ae^{t} + Bte^{t}\). However, we must remember that we are only guessing. If it doesn't work, keep guessing. Try: \(Ae^{t} + Bte^{t} + Ct^{2}e^{t}\)

OpenStudy (anonymous):

Thank you tkhunny! What is the method for coming up with the guesses?

OpenStudy (anonymous):

http://tutorial.math.lamar.edu/Classes/DE/UndeterminedCoefficients.aspx is the best website I have found so far documenting this method.

OpenStudy (anonymous):

There is in fact a formula for getting these guesses, but it's in my opinion rather complicated, I can see if I can find it again.

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