What is the solution for y^{''''}=625y ?

The solution for y^{''''}=625y is y=c_{1}e^{5t}+c_{2}e^{-5t}+c_{3}cos(5t)+c_{4}sin(5t)

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y^{''''}=625y

y^{^{''''}} = 625 y

y = c_{1} e^{5 t} + c_{2} e^{- 5 t} + c_{3} cos (5 t) + c_{4} sin (5 t)

Solution steps

y^{(4)} (t) = 625 y

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} e^{- 5 t} + c_{3} cos (5 t) + c_{4} sin (5 t)

y = c_{1} e^{5 t} + c_{2} e^{- 5 t} + c_{3} cos (5 t) + c_{4} sin (5 t)

2 y^{^{''}} + 8 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

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

\frac{d ^{2} y}{d x ^{2}} + 10 \frac{d y}{d x} + 41 y = 0

x^{^{''}} + x^{^{'}} - x = 0

\frac{d ^{3} y}{d x ^{3}} - y = 0

What is the solution for y^{''''}=625y ?
The solution for y^{''''}=625y is y=c_{1}e^{5t}+c_{2}e^{-5t}+c_{3}cos(5t)+c_{4}sin(5t)