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

The solution for y^{''''}+k^2y^{''}=0 is y=c_{1}+c_{2}t+c_{3}cos(kt)+c_{4}sin(kt)

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

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

y = c_{1} + c_{2} t + c_{3} cos (k t) + c_{4} sin (k t)

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} t + c_{3} cos (k t) + c_{4} sin (k t)

y = c_{1} + c_{2} t + c_{3} cos (k t) + c_{4} sin (k t)

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