What is the solution for y^{''}+18y^'+82y=0 ?

The solution for y^{''}+18y^'+82y=0 is y=e^{-9t}(c_{1}cos(t)+c_{2}sin(t))

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y^{''}+18y^'+82y=0

y^{^{''}} + 18 y^{^{'}} + 82 y = 0

y = e^{- 9 t} (c_{1} cos (t) + c_{2} sin (t))

Solution steps

y^{''} (t) + 18 y^{'} (t) + 82 y = 0

Solve linear ODE:

y = e^{- 9 t} (c_{1} cos (t) + c_{2} sin (t))

y = e^{- 9 t} (c_{1} cos (t) + c_{2} sin (t))

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What is the solution for y^{''}+18y^'+82y=0 ?
The solution for y^{''}+18y^'+82y=0 is y=e^{-9t}(c_{1}cos(t)+c_{2}sin(t))