I would like to know how to classify the following equations:

$y''+ 4y'+5y=2e^{-2x}cos(x)$.

Is it a second order linear equation?

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    $\begingroup$ See this. $\endgroup$ – Git Gud Apr 24 '15 at 23:30
  • $\begingroup$ @GitGud I did something similar, but I have (-2A+3Ax-3B+Bx=0) and -3A+Ax+2B-3Bx=2. Not too sure what to set x equal to in this case. $\endgroup$ – Chan Hunt Apr 25 '15 at 1:56

the characteristic equation is $$m^2+4m+5=0$$ $$m=-2\pm i$$ $$y_c=e^{-2x}[C_1\cos x+C_2\sin x]$$ now we should find the particular solution let $$y_p=e^{-2x}[A\cos x+B\sin x]$$ because the similarity between the particular and complementry soultions, so the particular solution should be multiplied by x $$y_p=xe^{-2x}[A\cos x+B\sin x]$$ then you can find the $A$ and $B$

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  • $\begingroup$ for the second one, how would i go about the change of variables, the website i was using to teach myself never covered change of variables. $\endgroup$ – Chan Hunt Apr 24 '15 at 23:46
  • $\begingroup$ @ForrestChanningHunter do do you mean about the particular solution $\endgroup$ – E.H.E Apr 24 '15 at 23:47
  • $\begingroup$ I can find A and B. I asked a second question starting with "the other one". not sure how to do change of variables here. The website I'm using never covered this. $\endgroup$ – Chan Hunt Apr 24 '15 at 23:52
  • $\begingroup$ There's no change of variables here $\endgroup$ – Dylan Apr 25 '15 at 4:19

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