What is the solution for y^{''''}+9y^{''}=20e^{-t} ?

The solution for y^{''''}+9y^{''}=20e^{-t} is y=c_{1}+c_{2}t+c_{3}cos(3t)+c_{4}sin(3t)+2e^{-t}

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

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

y = c_{1} + c_{2} t + c_{3} cos (3 t) + c_{4} sin (3 t) + 2 e^{- t}

Solution steps

y^{(4)} (t) + 9 y^{''} (t) = 20 e^{- t}

Solve linear ODE:

y = c_{1} + c_{2} t + c_{3} cos (3 t) + c_{4} sin (3 t) + 2 e^{- t}

y = c_{1} + c_{2} t + c_{3} cos (3 t) + c_{4} sin (3 t) + 2 e^{- t}

y^{^{''''}} - y = 9 t + cos (t)

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 4 e^{2 x}

4 y^{^{''}} - 8 y = 2

y^{^{''}} - y = 2.9 cos (t), y (0) = 0, y^{^{'}} (0) = 2.9

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} - 5 y = e^{x}

What is the solution for y^{''''}+9y^{''}=20e^{-t} ?
The solution for y^{''''}+9y^{''}=20e^{-t} is y=c_{1}+c_{2}t+c_{3}cos(3t)+c_{4}sin(3t)+2e^{-t}