The given system of differential equations is,
Putting the value of
in the third equation, we get,
Now differentiating both sides with respect to t, we get,
Putting
and the value of
in first equation, we get,
So the integrating factor of this differential equation is,
Hence the solution is,
Now putting this value of
in the given second differential equation, we get:
Integrating both sides, we get,