What is the solution for y^{''}+6y^'+13y=0,y(0)=-2,y^'(0)=0 ?

The solution for y^{''}+6y^'+13y=0,y(0)=-2,y^'(0)=0 is y=e^{-3t}(-2cos(2t)-3sin(2t))

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y^{''}+6y^'+13y=0,y(0)=-2,y^'(0)=0

y^{^{''}} + 6 y^{^{'}} + 13 y = 0, y (0) = - 2, y^{^{'}} (0) = 0

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

Solution steps

y^{''} (t) + 6 y^{'} (t) + 13 y = 0

Solve linear ODE:

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

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

What is the solution for y^{''}+6y^'+13y=0,y(0)=-2,y^'(0)=0 ?
The solution for y^{''}+6y^'+13y=0,y(0)=-2,y^'(0)=0 is y=e^{-3t}(-2cos(2t)-3sin(2t))