What is the solution for y^{''}+4y^'+13y=0,y(0)=2,y^'(0)=-2 ?

The solution for y^{''}+4y^'+13y=0,y(0)=2,y^'(0)=-2 is y=e^{-2t}(2cos(3t)+2/3 sin(3t))

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y^{''}+4y^'+13y=0,y(0)=2,y^'(0)=-2

y^{^{''}} + 4 y^{^{'}} + 13 y = 0, y (0) = 2, y^{^{'}} (0) = - 2

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

Solution steps

y^{''} (t) + 4 y^{'} (t) + 13 y = 0

Solve linear ODE:

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

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

What is the solution for y^{''}+4y^'+13y=0,y(0)=2,y^'(0)=-2 ?
The solution for y^{''}+4y^'+13y=0,y(0)=2,y^'(0)=-2 is y=e^{-2t}(2cos(3t)+2/3 sin(3t))