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Differential Equations

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The Expression of the Solution for an IVP

DIFFEQ-OECZFY

Which of the following is the solution for $y''+4y=2xe^{x}+x$ with $y(0)=1, y'(0)=-1$?

A

$y(x)=\frac{27}{25}\cos(2x)-\frac{157}{200}\sin(2x)+\frac{2}{5}xe^x-\frac{2}{25}e^x+\frac{x}{4}$

B

$y(x)=\cos(2x)-\frac{1}{2}\sin(2x)+\frac{2}{5}xe^x-\frac{2}{25}e^x+\frac{x}{4}$

C

$y(x)=\frac{29}{25}\cos(2x)-\frac{149}{200}\sin(2x)+\frac{2}{5}xe^x-\frac{4}{25}e^x+\frac{x}{4}$

D

$y(x)=\cos(2x)-\frac{1}{2}\sin(2x)+\frac{2}{5}xe^x-\frac{4}{25}e^x+\frac{x}{4}$