What is the solution for y^{''}+10y^'+61y=0 ?

The solution for y^{''}+10y^'+61y=0 is y=e^{-5t}(c_{1}cos(6t)+c_{2}sin(6t))

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y^{''}+10y^'+61y=0

y^{^{''}} + 10 y^{^{'}} + 61 y = 0

y = e^{- 5 t} (c_{1} cos (6 t) + c_{2} sin (6 t))

Solution steps

y^{''} (t) + 10 y^{'} (t) + 61 y = 0

Solve linear ODE:

y = e^{- 5 t} (c_{1} cos (6 t) + c_{2} sin (6 t))

y = e^{- 5 t} (c_{1} cos (6 t) + c_{2} sin (6 t))

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

x \to 4 - lim (\frac{3}{x - 2})

\int (x + \frac{1}{5 x}) d x

y = \frac{1}{12 x ^{2}}, y = x, y = \frac{x}{18}

\int \frac{3 x ^{5} - 6 x ^{2} + 2 x - 5}{x ^{3}} d x

What is the solution for y^{''}+10y^'+61y=0 ?
The solution for y^{''}+10y^'+61y=0 is y=e^{-5t}(c_{1}cos(6t)+c_{2}sin(6t))