What is the solution for y^{'''}+6y^{''}+11y^'+6y=0 ?

The solution for y^{'''}+6y^{''}+11y^'+6y=0 is y=c_{1}e^{-t}+c_{2}e^{-2t}+c_{3}e^{-3t}

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y^{'''}+6y^{''}+11y^'+6y=0

y^{^{'''}} + 6 y^{^{''}} + 11 y^{^{'}} + 6 y = 0

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

Solution steps

y^{'''} (t) + 6 y^{''} (t) + 11 y^{'} (t) + 6 y = 0

Solve linear ODE:

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

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

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What is the solution for y^{'''}+6y^{''}+11y^'+6y=0 ?
The solution for y^{'''}+6y^{''}+11y^'+6y=0 is y=c_{1}e^{-t}+c_{2}e^{-2t}+c_{3}e^{-3t}