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

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

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

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 \cdot e^{- t}

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - y^{^{'}} - a^{2} = 0

y^{^{''}} + 6 y^{^{'}} + 9 y = t + e^{3 t}

y^{^{''}} + 16 y = 5 cos (4 t), y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 9 y = 4, y^{1} (0) = e^{- 3 x}

y^{^{''''}} + 9 y^{^{''}} = 20 e^{- t}

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