What is the solution for y^{''''}=16y ?

The solution for y^{''''}=16y is y=c_{1}e^{2t}+c_{2}e^{-2t}+c_{3}cos(2t)+c_{4}sin(2t)

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y^{''''}=16y

y^{^{''''}} = 16 y

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

Solution steps

y^{(4)} (t) = 16 y

Solve linear ODE:

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

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

y^{^{'''}} + y^{^{''}} - 32 y^{^{'}} - 60 y = 0

4 y^{^{''}} + 19 y^{^{'}} - 5 y = 0

y^{^{''}} - 4 y^{^{'}} + 20 y = 0, y (0) = 0

y^{^{''}} + 6 y^{^{'}} + 13 y = 0, y (0) = - 2, y^{^{'}} (0) = 0

2 y^{^{''}} + 7 y^{^{'}} = 0

What is the solution for y^{''''}=16y ?
The solution for y^{''''}=16y is y=c_{1}e^{2t}+c_{2}e^{-2t}+c_{3}cos(2t)+c_{4}sin(2t)