What is the solution for y^{''''}-81y=0 ?

The solution for y^{''''}-81y=0 is y=c_{1}e^{3t}+c_{2}e^{-3t}+c_{3}cos(3t)+c_{4}sin(3t)

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y^{''''}-81y=0

y^{^{''''}} - 81 y = 0

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

Solution steps

y^{(4)} (t) - 81 y = 0

Solve linear ODE:

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

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

What is the solution for y^{''''}-81y=0 ?
The solution for y^{''''}-81y=0 is y=c_{1}e^{3t}+c_{2}e^{-3t}+c_{3}cos(3t)+c_{4}sin(3t)