What is the solution for 9y^{''}+18y^'+11y=0 ?

The solution for 9y^{''}+18y^'+11y=0 is y=e^{-t}(c_{1}cos((sqrt(2)t)/3)+c_{2}sin((sqrt(2)t)/3))

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9y^{''}+18y^'+11y=0

9 y^{^{''}} + 18 y^{^{'}} + 11 y = 0

y = e^{- t} (c_{1} cos (\frac{2 t}{3}) + c_{2} sin (\frac{2 t}{3}))

Solution steps

9 y^{''} (t) + 18 y^{'} (t) + 11 y = 0

Solve linear ODE:

y = e^{- t} (c_{1} cos (\frac{2 t}{3}) + c_{2} sin (\frac{2 t}{3}))

y = e^{- t} (c_{1} cos (\frac{2 t}{3}) + c_{2} sin (\frac{2 t}{3}))

What is the solution for 9y^{''}+18y^'+11y=0 ?
The solution for 9y^{''}+18y^'+11y=0 is y=e^{-t}(c_{1}cos((sqrt(2)t)/3)+c_{2}sin((sqrt(2)t)/3))