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{\partial}{\partial x} (\frac{4}{x})

- \frac{12}{s ^{5}}

\frac{2}{s ^{4}}

\int \frac{2}{( t + 4 ) ( t - 1 )} d t

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

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))