Write as
Where
Check if exact
Since then Not exact. Trying integrating factor , Since it is a function of alone, then it (1) can be made exact. The integrating factor is
Multiplying (1) by this integrating factor, now it becomes exact
Now we follow standard method for solving exact ODE. Let
From (2)
Substituting this into (3) to solve for
Hence the solution from (4) is
But , hence . Therefore, collecting constants into one, the solution is (implicit form)
From initial conditions
Hence final solution for in implicit form is