What is the solution for y^{''}+2y^'+11y=0 ?

The solution for y^{''}+2y^'+11y=0 is y=e^{-t}(c_{1}cos(sqrt(10)t)+c_{2}sin(sqrt(10)t))

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y^{''}+2y^'+11y=0

y^{^{''}} + 2 y^{^{'}} + 11 y = 0

y = e^{- t} (c_{1} cos (10 t) + c_{2} sin (10 t))

Solution steps

y^{''} (t) + 2 y^{'} (t) + 11 y = 0

Solve linear ODE:

y = e^{- t} (c_{1} cos (10 t) + c_{2} sin (10 t))

y = e^{- t} (c_{1} cos (10 t) + c_{2} sin (10 t))

y^{^{''}} - 17 y^{^{'}} + 72 y = 0, y (0) = 5, y^{^{'}} (0) = 0

y^{^{''}} - 9 y^{^{'}} - 14 y = 0

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

9 y^{^{''}} + 12 y^{^{'}} + 5 y = 0

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

What is the solution for y^{''}+2y^'+11y=0 ?
The solution for y^{''}+2y^'+11y=0 is y=e^{-t}(c_{1}cos(sqrt(10)t)+c_{2}sin(sqrt(10)t))