What is the solution for 0.25y^{''}+10y^'+1000y=0 ?

The solution for 0.25y^{''}+10y^'+1000y=0 is y=e^{-20t}(c_{1}cos(60t)+c_{2}sin(60t))

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0.25y^{''}+10y^'+1000y=0

0.25 y^{^{''}} + 10 y^{^{'}} + 1000 y = 0

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

Solution steps

0.25 y^{''} (t) + 10 y^{'} (t) + 1000 y = 0

Solve linear ODE:

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

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

y^{^{'''}} + y^{^{'}} = 0, y (0) = 1, y^{^{''}} (0) = 2

y^{^{''}} - 8 y^{^{''}} + 16 y = 0

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

6 y^{^{''}} + (- 5) y^{^{'}} + y = 0, y (0) = 4, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} + 13 y = 0

What is the solution for 0.25y^{''}+10y^'+1000y=0 ?
The solution for 0.25y^{''}+10y^'+1000y=0 is y=e^{-20t}(c_{1}cos(60t)+c_{2}sin(60t))