What is the solution for y^{'''}+18y^{''}+81y^'=0 ?

The solution for y^{'''}+18y^{''}+81y^'=0 is y=c_{1}+c_{2}e^{-9t}+c_{3}te^{-9t}

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y^{'''}+18y^{''}+81y^'=0

y^{^{'''}} + 18 y^{^{''}} + 81 y^{^{'}} = 0

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

Solution steps

y^{'''} (t) + 18 y^{''} (t) + 81 y^{'} (t) = 0

Solve linear ODE:

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

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

(5, - 1), (- 5, 5)

\frac{d}{d x} (3 x^{3} - 3 x + c)

\frac{d y}{d x} - 7 = 3 y - 7 x + 9

3 x - 1

\int + 5 arctan (\frac{1}{x}) d x

What is the solution for y^{'''}+18y^{''}+81y^'=0 ?
The solution for y^{'''}+18y^{''}+81y^'=0 is y=c_{1}+c_{2}e^{-9t}+c_{3}te^{-9t}