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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{\partial}{\partial x} (\frac{1}{2 cos ^{2} ( x )})

x \to \infty lim (arcsec (x))

\int 3 x^{2} + x d x

x \to 10 - lim (\frac{1}{( x - 10 ) ^{2}})

f (x) = e^{θ} sin (6 θ)

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