What is the solution for 256y^{''''}=16y ?

The solution for 256y^{''''}=16y is y=c_{1}e^{t/2}+c_{2}e^{-t/2}+c_{3}cos(t/2)+c_{4}sin(t/2)

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256y^{''''}=16y

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

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

Solution steps

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

Solve linear ODE:

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

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

What is the solution for 256y^{''''}=16y ?
The solution for 256y^{''''}=16y is y=c_{1}e^{t/2}+c_{2}e^{-t/2}+c_{3}cos(t/2)+c_{4}sin(t/2)