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

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

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625y^{''''}=y

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 14 y^{^{'}} = 0, y (0) = - 2, y^{^{'}} (0) = 14

y^{^{''}} + y^{^{'}} - 2 y = 0, y (0) = 4, y^{^{'}} (0) = 5

y^{^{''}} + 3 y^{^{'}} + 12 y = 0

\frac{4}{9} y^{^{''}} + 36 y = 0

2 y^{^{''}} + 5 y^{^{'}} + 3 y = 0, y (0) = 1, y^{^{'}} (0) = - 1.5

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