What is the solution for y^{''''}-k^2y^{''}=0 ?

The solution for y^{''''}-k^2y^{''}=0 is y=c_{1}e^{kt}+c_{2}e^{-kt}+c_{3}+c_{4}t

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

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

y = c_{1} e^{k t} + c_{2} e^{- k t} + c_{3} + c_{4} t

Solution steps

y^{(4)} (t) - k^{2} y^{''} (t) = 0

Solve linear ODE:

y = c_{1} e^{k t} + c_{2} e^{- k t} + c_{3} + c_{4} t

y = c_{1} e^{k t} + c_{2} e^{- k t} + c_{3} + c_{4} t

What is the solution for y^{''''}-k^2y^{''}=0 ?
The solution for y^{''''}-k^2y^{''}=0 is y=c_{1}e^{kt}+c_{2}e^{-kt}+c_{3}+c_{4}t