What is the solution for (d^2q)/(dt^2)+q^'+q=0 ?

The solution for (d^2q)/(dt^2)+q^'+q=0 is q=e^{-t/2}(c_{1}cos((sqrt(3)t)/2)+c_{2}sin((sqrt(3)t)/2))

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(d^2q)/(dt^2)+q^'+q=0

\frac{d ^{2} q}{d t ^{2}} + q^{^{'}} + q = 0

q = e^{- \frac{t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2}))

Solution steps

q^{''} (t) + q^{'} (t) + q = 0

Solve linear ODE:

q = e^{- \frac{t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2}))

q = e^{- \frac{t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2}))

16 \cdot y^{^{'''}} - y^{^{'}} = 0

y^{^{''}} - 6 y^{^{'}} + 10 y = 0, y (0) = - 1, y^{^{'}} (0) = 3

20 y^{^{''}} - 100 y^{^{'}} + 133 y = 0

y^{^{'''}} + 9 y^{^{'}} = 0, y^{^{''}} (0) = 27

x^{^{''}} + 6 x^{^{'}} + 8 x = 0, x (0) = 1, x^{^{'}} (0) = 2

What is the solution for (d^2q)/(dt^2)+q^'+q=0 ?
The solution for (d^2q)/(dt^2)+q^'+q=0 is q=e^{-t/2}(c_{1}cos((sqrt(3)t)/2)+c_{2}sin((sqrt(3)t)/2))