What is the solution for y^{''}+16y^'+80y=0 ?

The solution for y^{''}+16y^'+80y=0 is y=e^{-8t}(c_{1}cos(4t)+c_{2}sin(4t))

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y^{''}+16y^'+80y=0

y^{^{''}} + 16 y^{^{'}} + 80 y = 0

y = e^{- 8 t} (c_{1} cos (4 t) + c_{2} sin (4 t))

Solution steps

y^{''} (t) + 16 y^{'} (t) + 80 y = 0

Solve linear ODE:

y = e^{- 8 t} (c_{1} cos (4 t) + c_{2} sin (4 t))

y = e^{- 8 t} (c_{1} cos (4 t) + c_{2} sin (4 t))

\frac{d}{d x} (- x^{3} + 3 x^{2} + 9 x - 1)

e^{2 x}, - 2

\int \frac{1}{- x ^{2} + 249 x + 250} d x

x \to \infty lim (\frac{( ln ( 3 x ) )}{e ^{7 x}})

n = 0 \sum \infty (- 5)^{n}

What is the solution for y^{''}+16y^'+80y=0 ?
The solution for y^{''}+16y^'+80y=0 is y=e^{-8t}(c_{1}cos(4t)+c_{2}sin(4t))