What is the solution for y^{''}+6y^'+10y=0,y(0)=4 ?

The solution for y^{''}+6y^'+10y=0,y(0)=4 is y=e^{-3t}(4cos(t)+c_{2}sin(t))

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y^{''}+6y^'+10y=0,y(0)=4

y^{^{''}} + 6 y^{^{'}} + 10 y = 0, y (0) = 4

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

Solution steps

y^{''} (t) + 6 y^{'} (t) + 10 y = 0

Solve linear ODE:

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

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

What is the solution for y^{''}+6y^'+10y=0,y(0)=4 ?
The solution for y^{''}+6y^'+10y=0,y(0)=4 is y=e^{-3t}(4cos(t)+c_{2}sin(t))