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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

(y^{^{''}}) + y = 3 x sin (x)

y^{^{''}} + 500 y^{^{'}} + 20000 y = 1100

y^{^{''}} + 2 y^{^{'}} - 8 y = x + 1

y^{^{''}} - y^{^{'}} - 6 y = 15 sin (3 x)

y^{^{''}} - 4 y^{^{'}} + 3 y = 10 e^{3 x}

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