What is the solution for y^{''}+4y^'+4y=e^{-t} ?

The solution for y^{''}+4y^'+4y=e^{-t} is y=c_{1}e^{-2t}+c_{2}te^{-2t}+e^{-t}

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y^{''}+4y^'+4y=e^{-t}

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{- t}

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

Solution steps

y^{''} (t) + 4 y^{'} (t) + 4 y = e^{- t}

Solve linear ODE:

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

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

What is the solution for y^{''}+4y^'+4y=e^{-t} ?
The solution for y^{''}+4y^'+4y=e^{-t} is y=c_{1}e^{-2t}+c_{2}te^{-2t}+e^{-t}