# Help solving differential equations

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?

• See this. – Git Gud Apr 24 '15 at 23:30
• @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. – 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 $B$