What is the solution for y^{''}+12y^'+85y=0 ?

The solution for y^{''}+12y^'+85y=0 is y=e^{-6t}(c_{1}cos(7t)+c_{2}sin(7t))

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y^{''}+12y^'+85y=0

y^{^{''}} + 12 y^{^{'}} + 85 y = 0

y = e^{- 6 t} (c_{1} cos (7 t) + c_{2} sin (7 t))

Solution steps

y^{''} (t) + 12 y^{'} (t) + 85 y = 0

Solve linear ODE:

y = e^{- 6 t} (c_{1} cos (7 t) + c_{2} sin (7 t))

y = e^{- 6 t} (c_{1} cos (7 t) + c_{2} sin (7 t))

\int 2 e^{- 5 x} d x

- 2 x^{\frac{2}{3}} - 4

\int \frac{5 x ^{2}}{x + 7} d x

x \to 3 - lim (\frac{7}{x - 3})

x \to 0 lim (lo g_{e} (x^{2}))

What is the solution for y^{''}+12y^'+85y=0 ?
The solution for y^{''}+12y^'+85y=0 is y=e^{-6t}(c_{1}cos(7t)+c_{2}sin(7t))