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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 6 y^{^{'}} + 9 y = \frac{16 e ^{- 3 x}}{x ^{2} + 1}

y^{^{''}} - 2 y^{^{'}} = 30 e^{- 3 t}

y^{^{''}} - 2 y^{^{'}} + y = 5 x e^{x} sin (x)

y^{^{''}} + 4 y^{^{'}} + 3 y = 6 + e^{2 t}

y^{^{''}} + 12 y^{^{'}} + 37 y = 4 H (t)

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