What is the solution for 81y^{''}+18y^'+y=0 ?

The solution for 81y^{''}+18y^'+y=0 is y=c_{1}e^{-t/9}+c_{2}e^{-t/9}t

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81y^{''}+18y^'+y=0

81 y^{^{''}} + 18 y^{^{'}} + y = 0

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

Solution steps

81 y^{''} (t) + 18 y^{'} (t) + y = 0

Solve linear ODE:

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

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

What is the solution for 81y^{''}+18y^'+y=0 ?
The solution for 81y^{''}+18y^'+y=0 is y=c_{1}e^{-t/9}+c_{2}e^{-t/9}t