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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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