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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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