What is the solution for y^{''}+16y^'+65y=0 ?

The solution for y^{''}+16y^'+65y=0 is y=e^{-8t}(c_{1}cos(t)+c_{2}sin(t))

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y^{''}+16y^'+65y=0

y^{^{''}} + 16 y^{^{'}} + 65 y = 0

y = e^{- 8 t} (c_{1} cos (t) + c_{2} sin (t))

Solution steps

y^{''} (t) + 16 y^{'} (t) + 65 y = 0

Solve linear ODE:

y = e^{- 8 t} (c_{1} cos (t) + c_{2} sin (t))

y = e^{- 8 t} (c_{1} cos (t) + c_{2} sin (t))

\frac{d}{d x} (x^{2} - 25 ln (x^{2}))

f (x) = \frac{x}{x ^{2} - 6}

\int_{- 3}^{0} - x^{2} - 3 x d x

\int coth (x) d x

\int \frac{t}{t ^{3}} d t

What is the solution for y^{''}+16y^'+65y=0 ?
The solution for y^{''}+16y^'+65y=0 is y=e^{-8t}(c_{1}cos(t)+c_{2}sin(t))