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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 12 y^{^{'}} + 36 y = 0, y (0) = 3, y^{^{'}} (0) = \frac{39}{2}

y^{^{''}} + 18 y^{^{'}} + 80 y = 0, y (0) = 9, y^{^{'}} (0) = - 76

(D^{3} - 3 D) y = 0

(d - 5 d^{2} + 4 d - 20) x = 0

25 x^{^{''}} + 50 x^{^{'}} + 169 x = 0

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