What is the solution for y^{'''}+9y^{''}+27y^'+27y=0 ?

The solution for y^{'''}+9y^{''}+27y^'+27y=0 is y=c_{1}e^{-3t}+c_{2}te^{-3t}+c_{3}t^2e^{-3t}

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

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

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

Solution steps

y^{'''} (t) + 9 y^{''} (t) + 27 y^{'} (t) + 27 y = 0

Solve linear ODE:

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

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

What is the solution for y^{'''}+9y^{''}+27y^'+27y=0 ?
The solution for y^{'''}+9y^{''}+27y^'+27y=0 is y=c_{1}e^{-3t}+c_{2}te^{-3t}+c_{3}t^2e^{-3t}