What is the solution for x^{''}+5x^'+9x=0 ?

The solution for x^{''}+5x^'+9x=0 is x=e^{-(5t)/2}(c_{1}cos((sqrt(11)t)/2)+c_{2}sin((sqrt(11)t)/2))

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x^{''}+5x^'+9x=0

x^{^{''}} + 5 x^{^{'}} + 9 x = 0

x = e^{- \frac{5 t}{2}} (c_{1} cos (\frac{11 t}{2}) + c_{2} sin (\frac{11 t}{2}))

Solution steps

x^{''} (t) + 5 x^{'} (t) + 9 x = 0

Solve linear ODE:

x = e^{- \frac{5 t}{2}} (c_{1} cos (\frac{11 t}{2}) + c_{2} sin (\frac{11 t}{2}))

x = e^{- \frac{5 t}{2}} (c_{1} cos (\frac{11 t}{2}) + c_{2} sin (\frac{11 t}{2}))

25 y^{^{''}} - 30 y^{^{'}} + 9 y = 0, y^{1} (0) = e^{\frac{3 x}{5}}

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

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

5 y^{^{''}} + 5 y^{^{'}} + 45 y = 0, y (0) = - 8, y^{^{'}} (0) = 0

y^{^{''}} - \frac{10}{3} y^{^{'}} + α y = 0, y^{^{'}} (0) = - \frac{2}{3}

What is the solution for x^{''}+5x^'+9x=0 ?
The solution for x^{''}+5x^'+9x=0 is x=e^{-(5t)/2}(c_{1}cos((sqrt(11)t)/2)+c_{2}sin((sqrt(11)t)/2))