Move and arrange items so that xy'-2yy'=2x-y,

So (x-2y) y' = 2x-y.

This shows that x 2-xy+y 2 = c satisfies the differential equation (x-2y) y' = 2x-y.

That is, x 2-xy+y 2 = c is the solution of the differential equation (x-2y) y' = 2x-y.