What is the solution for y^{''}+y^'+5y=0,y(0)=0 ?

The solution for y^{''}+y^'+5y=0,y(0)=0 is y=c_{2}e^{-t/2}sin((sqrt(19)t)/2)

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

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

y = c_{2} e^{- \frac{t}{2}} sin (\frac{19 t}{2})

Solution steps

y^{''} (t) + y^{'} (t) + 5 y = 0

Solve linear ODE:

y = c_{2} e^{- \frac{t}{2}} sin (\frac{19 t}{2})

y = c_{2} e^{- \frac{t}{2}} sin (\frac{19 t}{2})

x^{^{''}} - 6 x^{^{'}} + 8 x = 0

2 y^{^{''}} + 2 y^{^{'}} - 2 y = 0

2 y^{^{''}} + 36 y^{^{'}} + 163 y = 0

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 25 y = 0

y^{^{'''}} - 3 y^{^{''}} + 4 y^{^{'}} - 2 y = 0

What is the solution for y^{''}+y^'+5y=0,y(0)=0 ?
The solution for y^{''}+y^'+5y=0,y(0)=0 is y=c_{2}e^{-t/2}sin((sqrt(19)t)/2)