What is the solution for 121y^{'''}+176y^{''}+64y^'=0 ?

The solution for 121y^{'''}+176y^{''}+64y^'=0 is y=c_{1}+c_{2}e^{-(8t)/(11)}+c_{3}e^{-(8t)/(11)}t

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121y^{'''}+176y^{''}+64y^'=0

121 y^{^{'''}} + 176 y^{^{''}} + 64 y^{^{'}} = 0

y = c_{1} + c_{2} e^{- \frac{8 t}{11}} + c_{3} e^{- \frac{8 t}{11}} t

Solution steps

121 y^{'''} (t) + 176 y^{''} (t) + 64 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- \frac{8 t}{11}} + c_{3} e^{- \frac{8 t}{11}} t

y = c_{1} + c_{2} e^{- \frac{8 t}{11}} + c_{3} e^{- \frac{8 t}{11}} t

\frac{d ^{2} y}{d x ^{2}} + 8 \cdot \frac{d y}{d x} + 5 \cdot y = 0

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 0, y^{^{'}} (0) = - 7

y^{^{''}} - y^{^{'}} - 6 y = 0, y (0) = 3, y^{^{'}} (0) = 4

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 9, y^{^{'}} (0) = 2

y^{^{''}} + 3 y^{^{'}} - 9 y = 0

What is the solution for 121y^{'''}+176y^{''}+64y^'=0 ?
The solution for 121y^{'''}+176y^{''}+64y^'=0 is y=c_{1}+c_{2}e^{-(8t)/(11)}+c_{3}e^{-(8t)/(11)}t