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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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