What is the solution for y^{''}+14y^'+85y=0 ?

The solution for y^{''}+14y^'+85y=0 is y=e^{-7t}(c_{1}cos(6t)+c_{2}sin(6t))

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y^{''}+14y^'+85y=0

y^{^{''}} + 14 y^{^{'}} + 85 y = 0

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

Solution steps

y^{''} (t) + 14 y^{'} (t) + 85 y = 0

Solve linear ODE:

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

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

\frac{3 x + 2}{4 x}

x \to 3 lim (x + 3 x - 3)

\int_{- 3}^{0} x 1 - x d x

\int 6 x e^{x} d x

\frac{d}{d x} (8^{x} ln (x))

What is the solution for y^{''}+14y^'+85y=0 ?
The solution for y^{''}+14y^'+85y=0 is y=e^{-7t}(c_{1}cos(6t)+c_{2}sin(6t))