What is the solution for y^{''}+20y^'+500y=0 ?

The solution for y^{''}+20y^'+500y=0 is y=e^{-10t}(c_{1}cos(20t)+c_{2}sin(20t))

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y^{''}+20y^'+500y=0

y^{^{''}} + 20 y^{^{'}} + 500 y = 0

y = e^{- 10 t} (c_{1} cos (20 t) + c_{2} sin (20 t))

Solution steps

y^{''} (t) + 20 y^{'} (t) + 500 y = 0

Solve linear ODE:

y = e^{- 10 t} (c_{1} cos (20 t) + c_{2} sin (20 t))

y = e^{- 10 t} (c_{1} cos (20 t) + c_{2} sin (20 t))

What is the solution for y^{''}+20y^'+500y=0 ?
The solution for y^{''}+20y^'+500y=0 is y=e^{-10t}(c_{1}cos(20t)+c_{2}sin(20t))