What is the solution for (d^4y)/(dt^4)-y=0 ?

The solution for (d^4y)/(dt^4)-y=0 is y=c_{1}e^t+c_{2}e^{-t}+c_{3}cos(t)+c_{4}sin(t)

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(d^4y)/(dt^4)-y=0

\frac{d ^{4} y}{d t ^{4}} - y = 0

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

Solution steps

\frac{d ^{4} y}{d t ^{4}} - y = 0

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''''}} - 8 y^{^{'}} = 0

y^{^{''}} - 4 y^{^{'}} = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 36 y = 0, y (\frac{π}{6}) = 1, y^{^{'}} (\frac{π}{6}) = - 2

y^{^{'''}} - y^{^{''}} - 24 y^{^{'}} - 36 y = 0

What is the solution for (d^4y)/(dt^4)-y=0 ?
The solution for (d^4y)/(dt^4)-y=0 is y=c_{1}e^t+c_{2}e^{-t}+c_{3}cos(t)+c_{4}sin(t)