What is the solution for y^{''''}-a^4y=0 ?

The solution for y^{''''}-a^4y=0 is y=c_{1}e^{at}+c_{2}e^{-at}+c_{3}cos(at)+c_{4}sin(at)

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y^{''''}-a^4y=0

y^{^{''''}} - a^{4} y = 0

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

Solution steps

y^{(4)} (t) - a^{4} y = 0

Solve linear ODE:

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

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

u^{^{''}} - a^{2} H (t) = 0

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

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

y^{^{''}} + 2 y^{^{'}} = 3 y

y^{^{'''}} + 7 y^{^{''}} - 5 y^{^{'}} - 75 y = 0

What is the solution for y^{''''}-a^4y=0 ?
The solution for y^{''''}-a^4y=0 is y=c_{1}e^{at}+c_{2}e^{-at}+c_{3}cos(at)+c_{4}sin(at)