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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} + 4 y = 0

y^{^{'''}} - 10 y^{^{''}} + 25 y^{^{'}} = 0

y^{^{''}} - 211 y^{^{'}} + 11 y = 0

4 y^{^{''}} + 16 y^{^{'}} + 17 y = 0

y^{^{''}} - (2 α - 1) y^{^{'}} + α (α - 1) y = 0

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