(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Write down the complementary solution [tex]y_c[/tex] and the correct particular solution [tex]y_p[/tex] in terms of its undetermined coefficients.

[tex]y^{'''}+y^{''}+3y^{'} -5y=x^2e^{x}+x^{2}e^{-x}cos(2x)+xe^{-x}sin(2x)[/tex]

3. The attempt at a solution

I can easily find [tex]y_c[/tex] but I dont understand [tex]y_p[/tex].

The solution is:TRY:[tex](Ax^2+Bx+C)e^x+e^{-x}[(Dx^2+Ex+F)cos(2x)+(Gx^2+Hx+I)sin(2x)][/tex]. And then you would adjust the particular solution. How come The [tex]Gx^2+Hx+I[/tex] term is a quadratic? If I didnt know the solution I would have put is as Gx+H.

If you had a good site explaining undetermined coefficients, that would be awesome, I dont really like the way the book explains it.

Thanks alot.

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# Differential Equation

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