What is the solution for x^{''''}-x=0 ?

The solution for x^{''''}-x=0 is x=c_{1}e^t+c_{2}e^{-t}+c_{3}cos(t)+c_{4}sin(t)

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

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

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

Solution steps

x^{(4)} (t) - x = 0

Solve linear ODE:

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

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

What is the solution for x^{''''}-x=0 ?
The solution for x^{''''}-x=0 is x=c_{1}e^t+c_{2}e^{-t}+c_{3}cos(t)+c_{4}sin(t)