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

The solution for y^{''}+4y^'+4y=e^x is y=c_{1}e^{-2x}+c_{2}xe^{-2x}+1/9 e^x

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

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

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{1}{9} e^{x}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{1}{9} e^{x}

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{1}{9} e^{x}

What is the solution for y^{''}+4y^'+4y=e^x ?
The solution for y^{''}+4y^'+4y=e^x is y=c_{1}e^{-2x}+c_{2}xe^{-2x}+1/9 e^x