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}

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} + y = 0

y^{^{''}} - 6 y^{^{'}} + 34 y = 0, y (0) = 5, y^{^{'}} (0) = - 5

y^{^{''}} - 10 y^{^{'}} + 50 y = 0, y (0) = - 4, y^{^{'}} (0) = - 5

9 y^{^{''}} - 12 y^{^{'}} + 4 y = 0, y (0) = e^{(\frac{2 x}{3})}

y^{^{''}} + 2 y^{^{'}} + (1 + \frac{9}{4} π^{2}) y = 0

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}