What is the solution for 34y+10y^'+y^{''}=0,y(0)=-3,y^'(0)=6 ?

The solution for 34y+10y^'+y^{''}=0,y(0)=-3,y^'(0)=6 is y=e^{-5t}(-3cos(3t)-3sin(3t))

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34y+10y^'+y^{''}=0,y(0)=-3,y^'(0)=6

34 y + 10 y^{^{'}} + y^{^{''}} = 0, y (0) = - 3, y^{^{'}} (0) = 6

y = e^{- 5 t} (- 3 cos (3 t) - 3 sin (3 t))

Solution steps

34 y + 10 y^{'} (t) + y^{''} (t) = 0

Solve linear ODE:

y = e^{- 5 t} (- 3 cos (3 t) - 3 sin (3 t))

y = e^{- 5 t} (- 3 cos (3 t) - 3 sin (3 t))

What is the solution for 34y+10y^'+y^{''}=0,y(0)=-3,y^'(0)=6 ?
The solution for 34y+10y^'+y^{''}=0,y(0)=-3,y^'(0)=6 is y=e^{-5t}(-3cos(3t)-3sin(3t))