What is the solution for y^{''}+2y^'=e^{-2x} ?

The solution for y^{''}+2y^'=e^{-2x} is y=c_{1}+c_{2}e^{-2x}-(e^{-2x}x)/2

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y^{''}+2y^'=e^{-2x}

y^{^{''}} + 2 y^{^{'}} = e^{- 2 x}

y = c_{1} + c_{2} e^{- 2 x} - \frac{e ^{- 2 x} x}{2}

Solution steps

y^{''} (x) + 2 y^{'} (x) = e^{- 2 x}

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 x} - \frac{e ^{- 2 x} x}{2}

y = c_{1} + c_{2} e^{- 2 x} - \frac{e ^{- 2 x} x}{2}

What is the solution for y^{''}+2y^'=e^{-2x} ?
The solution for y^{''}+2y^'=e^{-2x} is y=c_{1}+c_{2}e^{-2x}-(e^{-2x}x)/2