What is the solution for y^{''}+y^'+2y=0,y(0)=0 ?

The solution for y^{''}+y^'+2y=0,y(0)=0 is y=c_{2}e^{-t/2}sin((sqrt(7)t)/2)

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

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

y = c_{2} e^{- \frac{t}{2}} sin (\frac{7 t}{2})

Solution steps

y^{''} (t) + y^{'} (t) + 2 y = 0

Solve linear ODE:

y = c_{2} e^{- \frac{t}{2}} sin (\frac{7 t}{2})

y = c_{2} e^{- \frac{t}{2}} sin (\frac{7 t}{2})

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

y^{^{'''}} - 7 y^{^{'}} + 6 y = 0

16 y^{^{''''}} + 24 y^{^{''}} + 9 y = 0

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

(d^{3} - 3 d^{2} + 4) y = 0

What is the solution for y^{''}+y^'+2y=0,y(0)=0 ?
The solution for y^{''}+y^'+2y=0,y(0)=0 is y=c_{2}e^{-t/2}sin((sqrt(7)t)/2)