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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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