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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 1, y^{^{'}} (0) = 2

y^{^{''''}} - 6 y^{^{'''}} - 36 y^{^{''}} + 216 y^{^{'}} = 0

(D^{5} - 12 D^{3} + 16 D^{2}) y = 0

64 y^{^{''}} - y = 0

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

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