What is the solution for y^{''}+16y^'+73y=0 ?

The solution for y^{''}+16y^'+73y=0 is y=e^{-8t}(c_{1}cos(3t)+c_{2}sin(3t))

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y^{''}+16y^'+73y=0

y^{^{''}} + 16 y^{^{'}} + 73 y = 0

y = e^{- 8 t} (c_{1} cos (3 t) + c_{2} sin (3 t))

Solution steps

y^{''} (t) + 16 y^{'} (t) + 73 y = 0

Solve linear ODE:

y = e^{- 8 t} (c_{1} cos (3 t) + c_{2} sin (3 t))

y = e^{- 8 t} (c_{1} cos (3 t) + c_{2} sin (3 t))

y^{^{''}} - 8 y^{^{'}} + 4 y = 0

\frac{d y}{d x} = 2

\int e^{- x^{8}} (- 8 x^{7}) d x

\int tan^{2} (θ) cos (θ) d θ

x \to 16 lim (\frac{x ^{2}}{2} - \frac{8}{x})

What is the solution for y^{''}+16y^'+73y=0 ?
The solution for y^{''}+16y^'+73y=0 is y=e^{-8t}(c_{1}cos(3t)+c_{2}sin(3t))