What is the solution for y^{''}-3y^'-4y=3e^{-t} ?

The solution for y^{''}-3y^'-4y=3e^{-t} is y=c_{1}e^{4t}+c_{2}e^{-t}-(3e^{-t}t)/5

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y^{''}-3y^'-4y=3e^{-t}

y^{^{''}} - 3 y^{^{'}} - 4 y = 3 e^{- t}

y = c_{1} e^{4 t} + c_{2} e^{- t} - \frac{3 e ^{- t} t}{5}

Solution steps

y^{''} (t) - 3 y^{'} (t) - 4 y = 3 e^{- t}

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} e^{- t} - \frac{3 e ^{- t} t}{5}

y = c_{1} e^{4 t} + c_{2} e^{- t} - \frac{3 e ^{- t} t}{5}

What is the solution for y^{''}-3y^'-4y=3e^{-t} ?
The solution for y^{''}-3y^'-4y=3e^{-t} is y=c_{1}e^{4t}+c_{2}e^{-t}-(3e^{-t}t)/5