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

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

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

y^{^{''''}} + k^{2} \cdot 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} \cdot 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)

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (- 1) = 6, y^{^{'}} (- 1) = 5

y^{^{''}} - a \cdot y^{^{'}} - b \cdot y = 0

9 y^{^{''}} - 12 y^{^{'}} + 29 y = 0, y (0) = 1, y^{^{'}} (1) = 3

y^{^{''}} + 8 y^{^{'}} + 24 y = 0

y^{^{'''}} - 9 y^{^{''}} + 25 y^{^{'}} - 17 y = 0

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