What is the solution for y^{''}+120y^'+10000y=0 ?

The solution for y^{''}+120y^'+10000y=0 is y=e^{-60t}(c_{1}cos(80t)+c_{2}sin(80t))

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y^{''}+120y^'+10000y=0

y^{^{''}} + 120 y^{^{'}} + 10000 y = 0

y = e^{- 60 t} (c_{1} cos (80 t) + c_{2} sin (80 t))

Solution steps

y^{''} (t) + 120 y^{'} (t) + 10000 y = 0

Solve linear ODE:

y = e^{- 60 t} (c_{1} cos (80 t) + c_{2} sin (80 t))

y = e^{- 60 t} (c_{1} cos (80 t) + c_{2} sin (80 t))

y^{^{'''}} - 18 y^{^{''}} + 108 y^{^{'}} - 216 y = 0

y^{^{''}} + 6 \cdot 0 + 16 y = 0

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

y^{^{''}} - \frac{1}{r ^{2}} y = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (1) = e^{2 x}

What is the solution for y^{''}+120y^'+10000y=0 ?
The solution for y^{''}+120y^'+10000y=0 is y=e^{-60t}(c_{1}cos(80t)+c_{2}sin(80t))