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

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

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

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

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

Solution steps

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

\int ln (1 + \frac{1}{x ^{2}}) d x

\int (3 x + 1)^{\frac{1}{2}} d x

\frac{d}{d x} ((3 - 2 x)^{2})

f (x) = \frac{2 x}{x ^{2} + 1}, (- 1, - 1)

\frac{2 ( x + 1 )}{x ^{2} + 1}

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