What is the solution for y^{''}+6y^'+90y=0 ?

The solution for y^{''}+6y^'+90y=0 is y=e^{-3t}(c_{1}cos(9t)+c_{2}sin(9t))

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y^{''}+6y^'+90y=0

y^{^{''}} + 6 y^{^{'}} + 90 y = 0

y = e^{- 3 t} (c_{1} cos (9 t) + c_{2} sin (9 t))

Solution steps

y^{''} (t) + 6 y^{'} (t) + 90 y = 0

Solve linear ODE:

y = e^{- 3 t} (c_{1} cos (9 t) + c_{2} sin (9 t))

y = e^{- 3 t} (c_{1} cos (9 t) + c_{2} sin (9 t))

What is the solution for y^{''}+6y^'+90y=0 ?
The solution for y^{''}+6y^'+90y=0 is y=e^{-3t}(c_{1}cos(9t)+c_{2}sin(9t))