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

The solution for y^{''}+2y^'+y=4e^{-2t}+t+t^2 is y=c_{1}e^{-t}+c_{2}te^{-t}+4e^{-2t}+t^2-3t+4

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y^{''}+2y^'+y=4e^{-2t}+t+t^2

y^{^{''}} + 2 y^{^{'}} + y = 4 e^{- 2 t} + t + t^{2}

y = c_{1} e^{- t} + c_{2} t e^{- t} + 4 e^{- 2 t} + t^{2} - 3 t + 4

Solution steps

y^{''} (t) + 2 y^{'} (t) + y = 4 e^{- 2 t} + t + t^{2}

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} t e^{- t} + 4 e^{- 2 t} + t^{2} - 3 t + 4

y = c_{1} e^{- t} + c_{2} t e^{- t} + 4 e^{- 2 t} + t^{2} - 3 t + 4

What is the solution for y^{''}+2y^'+y=4e^{-2t}+t+t^2 ?
The solution for y^{''}+2y^'+y=4e^{-2t}+t+t^2 is y=c_{1}e^{-t}+c_{2}te^{-t}+4e^{-2t}+t^2-3t+4