What is the solution for y^{''}-y=4e^{-x} ?

The solution for y^{''}-y=4e^{-x} is y=c_{1}e^x+c_{2}e^{-x}-2xe^{-x}

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y^{''}-y=4e^{-x}

y^{^{''}} - y = 4 e^{- x}

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

Solution steps

y^{''} (x) - y = 4 e^{- x}

Solve linear ODE:

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

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

What is the solution for y^{''}-y=4e^{-x} ?
The solution for y^{''}-y=4e^{-x} is y=c_{1}e^x+c_{2}e^{-x}-2xe^{-x}