What is the solution for y^{''}+2y^'+10y=0,y(0)=4,y^'(0)=-2 ?

The solution for y^{''}+2y^'+10y=0,y(0)=4,y^'(0)=-2 is y=e^{-t}(4cos(3t)+2/3 sin(3t))

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y^{''}+2y^'+10y=0,y(0)=4,y^'(0)=-2

y^{^{''}} + 2 y^{^{'}} + 10 y = 0, y (0) = 4, y^{^{'}} (0) = - 2

y = e^{- t} (4 cos (3 t) + \frac{2}{3} sin (3 t))

Solution steps

y^{''} (t) + 2 y^{'} (t) + 10 y = 0

Solve linear ODE:

y = e^{- t} (4 cos (3 t) + \frac{2}{3} sin (3 t))

y = e^{- t} (4 cos (3 t) + \frac{2}{3} sin (3 t))

What is the solution for y^{''}+2y^'+10y=0,y(0)=4,y^'(0)=-2 ?
The solution for y^{''}+2y^'+10y=0,y(0)=4,y^'(0)=-2 is y=e^{-t}(4cos(3t)+2/3 sin(3t))