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

The solution for y^{''''}-9y^{''}=0 is y=c_{1}e^{3t}+c_{2}e^{-3t}+c_{3}+c_{4}t

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 11 y^{^{'}} + 18 y = 0

y^{^{'''}} + 9 y^{^{''}} + 27 y^{^{'}} + 27 y = 0

2 y^{^{''}} - 3 y^{^{'}} + 5 y = 0

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 0, y (0) = 2, y^{^{'}} (0) = 2

y^{^{''}} + y^{^{'}} = 0, y (0) = cos (x)

What is the solution for y^{''''}-9y^{''}=0 ?
The solution for y^{''''}-9y^{''}=0 is y=c_{1}e^{3t}+c_{2}e^{-3t}+c_{3}+c_{4}t