Solve the given differential equation by undetermined coefficients.

$y^{\text{'}\text{'}}2y^{\text{'}}=2x5-e^{-2x}$

Possible Answers

$($a$.)y=C_1+C_2{e}^{-2x}{x}^{2}5x-\frac{1}{2}{e}^{-2x}$

$($b$.)y=C_1+C_2{e}^{-2x}\frac{1}{2}{x}^{2}2x\frac{1}{2}x{e}^{-2x}$

$($c$.)y=C_1+C_2{e}^{-2x}\frac{1}{2}{x}^{2}2x-\frac{1}{2}{e}^{-2x}$

$($d$.)y=C_1+C_2{e}^{-2x}\frac{1}{2}{x}^{2}x\frac{1}{2}{e}^{-2x}$

$($e$.)$ None of the above

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