What is the solution for y^{''}+y^'+3y=0 ?

The solution for y^{''}+y^'+3y=0 is y=e^{-t/2}(c_{1}cos((sqrt(11)t)/2)+c_{2}sin((sqrt(11)t)/2))

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y^{''}+y^'+3y=0

y^{^{''}} + y^{^{'}} + 3 y = 0

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

Solution steps

y^{''} (t) + y^{'} (t) + 3 y = 0

Solve linear ODE:

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

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

d er i v a t i v e f (x) = (2 x^{2} - x + 1) \cdot (x^{2} + 2 x + 3)

\int \frac{1}{( x - 1 ) ( x + 4 )} d x

d er i v a t i v e x^{2} \cdot arctan (x)

y^{^{'}} = a y + b

\int \frac{1}{x ^{2}} x^{'} d x

What is the solution for y^{''}+y^'+3y=0 ?
The solution for y^{''}+y^'+3y=0 is y=e^{-t/2}(c_{1}cos((sqrt(11)t)/2)+c_{2}sin((sqrt(11)t)/2))