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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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