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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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