What is the solution for y^{''}+3y^'+2y=e^{-t} ?

The solution for y^{''}+3y^'+2y=e^{-t} is y=c_{1}e^{-t}+c_{2}e^{-2t}+e^{-t}t

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y^{''}+3y^'+2y=e^{-t}

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{- t}

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

Solution steps

y^{''} (t) + 3 y^{'} (t) + 2 y = e^{- t}

Solve linear ODE:

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

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

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What is the solution for y^{''}+3y^'+2y=e^{-t} ?
The solution for y^{''}+3y^'+2y=e^{-t} is y=c_{1}e^{-t}+c_{2}e^{-2t}+e^{-t}t