What is the solution for 64y^{''}+144y^'+81y=0 ?

The solution for 64y^{''}+144y^'+81y=0 is y=c_{1}e^{-(9t)/8}+c_{2}e^{-(9t)/8}t

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64y^{''}+144y^'+81y=0

64 y^{^{''}} + 144 y^{^{'}} + 81 y = 0

y = c_{1} e^{- \frac{9 t}{8}} + c_{2} e^{- \frac{9 t}{8}} t

Solution steps

64 y^{''} (t) + 144 y^{'} (t) + 81 y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{9 t}{8}} + c_{2} e^{- \frac{9 t}{8}} t

y = c_{1} e^{- \frac{9 t}{8}} + c_{2} e^{- \frac{9 t}{8}} t

\frac{10}{s ^{2} + s + 10} \cdot \frac{1}{s}

\frac{\partial}{\partial x} (\frac{e ^{y}}{x + y ^{5}})

\frac{\partial}{\partial x} (cos (2 c x + a c t))

\frac{d}{d x} (1000 (1 - \frac{x}{60})^{2})

y^{^{'}} = 1 + \frac{y}{x}

What is the solution for 64y^{''}+144y^'+81y=0 ?
The solution for 64y^{''}+144y^'+81y=0 is y=c_{1}e^{-(9t)/8}+c_{2}e^{-(9t)/8}t