What is the solution for 81y^{''''}=y ?

The solution for 81y^{''''}=y is y=c_{1}e^{t/3}+c_{2}e^{-t/3}+c_{3}cos(t/3)+c_{4}sin(t/3)

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81y^{''''}=y

81 y^{^{''''}} = y

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 7 y^{^{'}} + 12 y = 0, y (0) = 0, y^{^{'}} (0) = 3

y^{^{''}} + \frac{5}{2} y^{^{'}} + 1.578125 y = 0

u^{^{''}} + \frac{2}{r} u^{^{'}} = 0

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

y^{^{''}} - 2 y^{^{'}} - 195 y = 0, y (0) = 10, y^{^{'}} (0) = - 46

What is the solution for 81y^{''''}=y ?
The solution for 81y^{''''}=y is y=c_{1}e^{t/3}+c_{2}e^{-t/3}+c_{3}cos(t/3)+c_{4}sin(t/3)