What is the solution for 66y^{'''}+17y^{''}+y^'=0 ?

The solution for 66y^{'''}+17y^{''}+y^'=0 is y=c_{1}+c_{2}e^{-t/(11)}+c_{3}e^{-t/6}

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66y^{'''}+17y^{''}+y^'=0

66 y^{^{'''}} + 17 y^{^{''}} + y^{^{'}} = 0

y = c_{1} + c_{2} e^{- \frac{t}{11}} + c_{3} e^{- \frac{t}{6}}

Solution steps

66 y^{'''} (t) + 17 y^{''} (t) + y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- \frac{t}{11}} + c_{3} e^{- \frac{t}{6}}

y = c_{1} + c_{2} e^{- \frac{t}{11}} + c_{3} e^{- \frac{t}{6}}

y^{^{'''}} - 15 y^{^{''}} + 27 y^{^{'}} + 243 y = 0

\frac{d ^{2} y}{d x ^{2}} (1) - \frac{d y}{d x} (5) + 4 y = 0

2 x^{^{''}} + 2 x^{^{'}} + 3 x = 0

y^{^{''}} + a y = 0, y^{^{'}} (0) = 0, y (1) = 0

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

What is the solution for 66y^{'''}+17y^{''}+y^'=0 ?
The solution for 66y^{'''}+17y^{''}+y^'=0 is y=c_{1}+c_{2}e^{-t/(11)}+c_{3}e^{-t/6}