What is the solution for y^{''''}+9y^{''}=0 ?

The solution for y^{''''}+9y^{''}=0 is y=c_{1}+c_{2}t+c_{3}cos(3t)+c_{4}sin(3t)

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y^{''''}+9y^{''}=0

y^{^{''''}} + 9 y^{^{''}} = 0

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

Solution steps

y^{(4)} (t) + 9 y^{''} (t) = 0

Solve linear ODE:

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

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

25 y^{^{''}} - 120 y^{^{'}} + 144 y = 0

y^{^{'''}} - 7 y^{^{''}} + 16 y^{^{'}} - 12 y = 0

2 y^{^{''}} + 4 y^{^{'}} + 4 y = 0

y^{^{''}} - 4 y^{^{'}} + y = 0, y (0) = 3, y^{^{'}} (0) = 5

y^{^{'''}} + y^{^{''}} + 4 y^{^{'}} + 4 y = 0

What is the solution for y^{''''}+9y^{''}=0 ?
The solution for y^{''''}+9y^{''}=0 is y=c_{1}+c_{2}t+c_{3}cos(3t)+c_{4}sin(3t)