What is the solution for 81y^{''}+72y^'+16y=0 ?

The solution for 81y^{''}+72y^'+16y=0 is y=c_{1}e^{-(4t)/9}+c_{2}e^{-(4t)/9}t

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81y^{''}+72y^'+16y=0

81 y^{^{''}} + 72 y^{^{'}} + 16 y = 0

y = c_{1} e^{- \frac{4 t}{9}} + c_{2} e^{- \frac{4 t}{9}} t

Solution steps

81 y^{''} (t) + 72 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = c_{1} e^{- \frac{4 t}{9}} + c_{2} e^{- \frac{4 t}{9}} t

y = c_{1} e^{- \frac{4 t}{9}} + c_{2} e^{- \frac{4 t}{9}} t

\frac{d y}{d x} = \frac{1 - y}{1 + x ^{2}}

- 2 x^{2}, at x = 1

y = sin (e^{x})

x \to \infty lim (- x e^{1 - x})

\int \frac{7 r ^{2}}{r + 3} d r

What is the solution for 81y^{''}+72y^'+16y=0 ?
The solution for 81y^{''}+72y^'+16y=0 is y=c_{1}e^{-(4t)/9}+c_{2}e^{-(4t)/9}t