What is the solution for 2y^{''}+8y^'+80y=0 ?

The solution for 2y^{''}+8y^'+80y=0 is y=e^{-2t}(c_{1}cos(6t)+c_{2}sin(6t))

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2y^{''}+8y^'+80y=0

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 0

y = e^{- 2 t} (c_{1} cos (6 t) + c_{2} sin (6 t))

Solution steps

2 y^{''} (t) + 8 y^{'} (t) + 80 y = 0

Solve linear ODE:

y = e^{- 2 t} (c_{1} cos (6 t) + c_{2} sin (6 t))

y = e^{- 2 t} (c_{1} cos (6 t) + c_{2} sin (6 t))

What is the solution for 2y^{''}+8y^'+80y=0 ?
The solution for 2y^{''}+8y^'+80y=0 is y=e^{-2t}(c_{1}cos(6t)+c_{2}sin(6t))