What is the solution for y^{''}+y^'+9.5y=0 ?

The solution for y^{''}+y^'+9.5y=0 is y=e^{-t/2}(c_{1}cos((sqrt(37)t)/2)+c_{2}sin((sqrt(37)t)/2))

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y^{''}+y^'+9.5y=0

y^{^{''}} + y^{^{'}} + 9.5 y = 0

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{37 t}{2}) + c_{2} sin (\frac{37 t}{2}))

Solution steps

y^{''} (t) + y^{'} (t) + 9.5 y = 0

Solve linear ODE:

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{37 t}{2}) + c_{2} sin (\frac{37 t}{2}))

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{37 t}{2}) + c_{2} sin (\frac{37 t}{2}))

y^{^{''}} + 16 y = 0, y (π^{8}) = - 2, y^{^{'}} (π^{8}) = 16

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

y^{^{''}} - \frac{10}{3} y^{^{'}} + α y = 0

(y^{^{''}} + 4 y)^{4} = 0

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

What is the solution for y^{''}+y^'+9.5y=0 ?
The solution for y^{''}+y^'+9.5y=0 is y=e^{-t/2}(c_{1}cos((sqrt(37)t)/2)+c_{2}sin((sqrt(37)t)/2))