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}

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}