What is the solution for 1/4 x^{''}+10x^'+1000x=0 ?

The solution for 1/4 x^{''}+10x^'+1000x=0 is x=e^{-20t}(c_{1}cos(60t)+c_{2}sin(60t))

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1/4 x^{''}+10x^'+1000x=0

\frac{1}{4} x^{^{''}} + 10 x^{^{'}} + 1000 x = 0

x = e^{- 20 t} (c_{1} cos (60 t) + c_{2} sin (60 t))

Solution steps

\frac{1}{4} x^{''} (t) + 10 x^{'} (t) + 1000 x = 0

Solve linear ODE:

x = e^{- 20 t} (c_{1} cos (60 t) + c_{2} sin (60 t))

x = e^{- 20 t} (c_{1} cos (60 t) + c_{2} sin (60 t))

What is the solution for 1/4 x^{''}+10x^'+1000x=0 ?
The solution for 1/4 x^{''}+10x^'+1000x=0 is x=e^{-20t}(c_{1}cos(60t)+c_{2}sin(60t))