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

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

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

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

y = c_{1} + c_{2} e^{- 4 x} + x + e^{- 4 x} x

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- 4 x} + x + e^{- 4 x} x

y = c_{1} + c_{2} e^{- 4 x} + x + e^{- 4 x} x

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