Differentiating: sec^2(x-y)(1-dy/dx)=((1+x^2)dy/dx-2xy)/(1+x^2)^2;
sec^2(x-y)=1+tan^2(x-y), so (1+tan^2(x-y))(1-dy/dx)=dy/dx/(1+x^2)-2xy/(1+x^2)^2.
tan^2(x-y)=y^2/(1+x^2)^2,
therefore (1+y^2/(1+x^2)^2)(1-dy/dx)=
1-dy/dx+y^2/(1+x^2)^2-y^2dy/dx/(1+x^2)^2=dy/dx/(1+x^2)-2xy/(1+x^2)^2;
dy/dx(1+y^2/(1+x^2)^2+1/(1+x^2))=(y^2+2xy)/(1+x^2)^2;
dy/dx((1+x^2)^2+y^2+1+x^2)=y(y+2x); dy/dx=y(y+2x)/(3x^2+x^4+y^2+2).