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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

x^{^{''}} + 6 x^{^{'}} + 9 x = 0, x (0) = b

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 1, y^{^{'}} (0) = 1

x^{^{''}} + 16 x = 0, x (0) = - 1, x^{^{'}} (0) = - 5

3 y^{^{''}} + 11 y^{^{'}} - 4 y = 0

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 30 y = 0

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