What is the solution for y^{''}+12y^'+117y=0 ?

The solution for y^{''}+12y^'+117y=0 is y=e^{-6t}(c_{1}cos(9t)+c_{2}sin(9t))

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y^{''}+12y^'+117y=0

y^{^{''}} + 12 y^{^{'}} + 117 y = 0

y = e^{- 6 t} (c_{1} cos (9 t) + c_{2} sin (9 t))

Solution steps

y^{''} (t) + 12 y^{'} (t) + 117 y = 0

Solve linear ODE:

y = e^{- 6 t} (c_{1} cos (9 t) + c_{2} sin (9 t))

y = e^{- 6 t} (c_{1} cos (9 t) + c_{2} sin (9 t))

\frac{\partial}{\partial x} (2 x - \frac{3}{x ^{2}} + y)

d er i v a t i v e y = 2 - x

y^{^{''}} - y^{^{'}} + 5 y = 3

\frac{d}{d x} (2 (1 - x))

y^{^{''}} + 4 y = x^{2} + 3 e^{x}

What is the solution for y^{''}+12y^'+117y=0 ?
The solution for y^{''}+12y^'+117y=0 is y=e^{-6t}(c_{1}cos(9t)+c_{2}sin(9t))