Solving a Differential Equation By Regrouping Terms

The differential equation  
  with the curve passing through  
  cannot be solved by separation of variables, use of integrating factors, parts, substitution,...
If we expand the brackets and rearrange however we get

We can write this as  
Integration now gives  
The curve passes through  
\[2^2+1^2-2 \times 2 \times 1=1=c\]
  and the solution is