What is the solution for y^{''}+3y^'+5y=0,y(0)=0,y^'(0)=1 ?

The solution for y^{''}+3y^'+5y=0,y(0)=0,y^'(0)=1 is y= 2/(sqrt(11))e^{-(3t)/2}sin((sqrt(11)t)/2)

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y^{''}+3y^'+5y=0,y(0)=0,y^'(0)=1

y^{^{''}} + 3 y^{^{'}} + 5 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y = \frac{2}{11} e^{- \frac{3 t}{2}} sin (\frac{11 t}{2})

Solution steps

y^{''} (t) + 3 y^{'} (t) + 5 y = 0

Solve linear ODE:

y = \frac{2}{11} e^{- \frac{3 t}{2}} sin (\frac{11 t}{2})

y = \frac{2}{11} e^{- \frac{3 t}{2}} sin (\frac{11 t}{2})

What is the solution for y^{''}+3y^'+5y=0,y(0)=0,y^'(0)=1 ?
The solution for y^{''}+3y^'+5y=0,y(0)=0,y^'(0)=1 is y= 2/(sqrt(11))e^{-(3t)/2}sin((sqrt(11)t)/2)