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))

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

f (x) = \frac{1}{x ^{6}}

\frac{\partial}{\partial y} (y^{2} + y)

\int 10 tan^{3} (x) sec (x) d x

\int \frac{x ^{2} + 1}{x} d x

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))