What is the solution for y^{''''}=256y ?

The solution for y^{''''}=256y is y=c_{1}e^{4t}+c_{2}e^{-4t}+c_{3}cos(4t)+c_{4}sin(4t)

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y^{''''}=256y

y^{^{''''}} = 256 y

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

Solution steps

y^{(4)} (t) = 256 y

Solve linear ODE:

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

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

\frac{1}{2} y^{^{''}} - y^{^{'}} = 0

y^{^{''}} + y^{^{'}} + 2 y = 0, y^{^{'}} (0) = - 2, y (0) = 1

2 y^{^{''}} - 3 y^{^{'}} + 8 y = 0

y^{^{''}} + 14 y^{^{'}} + 49 y = 0, y (0) = - 1, y^{^{'}} (0) = 1

y^{^{''''}} - 3 y^{^{'''}} - 4 y^{^{''}} = 0

What is the solution for y^{''''}=256y ?
The solution for y^{''''}=256y is y=c_{1}e^{4t}+c_{2}e^{-4t}+c_{3}cos(4t)+c_{4}sin(4t)