What is the solution for y^{''''}-81y^{''}=0 ?

The solution for y^{''''}-81y^{''}=0 is y=c_{1}e^{9t}+c_{2}e^{-9t}+c_{3}+c_{4}t

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y^{''''}-81y^{''}=0

y^{^{''''}} - 81 y^{^{''}} = 0

y = c_{1} e^{9 t} + c_{2} e^{- 9 t} + c_{3} + c_{4} t

Solution steps

y^{(4)} (t) - 81 y^{''} (t) = 0

Solve linear ODE:

y = c_{1} e^{9 t} + c_{2} e^{- 9 t} + c_{3} + c_{4} t

y = c_{1} e^{9 t} + c_{2} e^{- 9 t} + c_{3} + c_{4} t

3.5 y^{^{''}} - 5.6 y^{^{'}} + 2.2 y = 0

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

\frac{1}{4} y^{^{''}} + 2 y^{^{'}} + 2 y = 0

\frac{d ^{2} y}{d t ^{2}} + 25 y = 0

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

What is the solution for y^{''''}-81y^{''}=0 ?
The solution for y^{''''}-81y^{''}=0 is y=c_{1}e^{9t}+c_{2}e^{-9t}+c_{3}+c_{4}t