What is the solution for y^{''}+16y^'+80y=0 ?

The solution for y^{''}+16y^'+80y=0 is y=e^{-8t}(c_{1}cos(4t)+c_{2}sin(4t))

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y^{''}+16y^'+80y=0

y^{^{''}} + 16 y^{^{'}} + 80 y = 0

y = e^{- 8 t} (c_{1} cos (4 t) + c_{2} sin (4 t))

Solution steps

y^{''} (t) + 16 y^{'} (t) + 80 y = 0

Solve linear ODE:

y = e^{- 8 t} (c_{1} cos (4 t) + c_{2} sin (4 t))

y = e^{- 8 t} (c_{1} cos (4 t) + c_{2} sin (4 t))

What is the solution for y^{''}+16y^'+80y=0 ?
The solution for y^{''}+16y^'+80y=0 is y=e^{-8t}(c_{1}cos(4t)+c_{2}sin(4t))