What is the solution for y^{''}+6y^'+16y=0 ?

The solution for y^{''}+6y^'+16y=0 is y=e^{-3t}(c_{1}cos(sqrt(7)t)+c_{2}sin(sqrt(7)t))

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

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

y = e^{- 3 t} (c_{1} cos (7 t) + c_{2} sin (7 t))

Solution steps

y^{''} (t) + 6 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = e^{- 3 t} (c_{1} cos (7 t) + c_{2} sin (7 t))

y = e^{- 3 t} (c_{1} cos (7 t) + c_{2} sin (7 t))

5 y^{^{''}} + 20 y = 0

(D^{4} - 2 D^{2} + 4) y = 0

4 y^{^{''}} - 8 y^{^{'}} + 3 y = 0, y (0) = 2, y^{^{'}} (0) = 1

2 y^{^{''}} + 4 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

2 y^{^{''}} + y = 0, y (0) = e^{- \frac{x}{2}}

What is the solution for y^{''}+6y^'+16y=0 ?
The solution for y^{''}+6y^'+16y=0 is y=e^{-3t}(c_{1}cos(sqrt(7)t)+c_{2}sin(sqrt(7)t))