Solving a Differential Equation By Regrouping Terms
\[(2x-y)dx+(2y-x)dx=0\]with the curve passing through
\[(2,1)\]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