The equation can be rewritten: x^2dx/(1-x)=ydy.
x^2/(1-x) or -x^2/(x-1)=-(1+x+1/(x-1)) so -∫(1+x+1/(x-1))dx=∫ydy=y^2/2.
That is: -(x+x^2/2+ln|x-1|)=y^2/2 plus constant of integration, which can be absorbed into the log:
-(x+x^2/2+ln|A(x-1)|)=y^2/2, where A is a constant. There are several ways of writing this solution. An explicit way is to make y the subject (the output), but the implicit form describes the relationship between x and y concisely: (x^2+y^2)/2+x+ln|A(x-1)|=0 or x^2+y^2+2x+2ln|A(x-1)|=0.