y(1+x^2)dy=x(y^2-1)dx
ydy/(y^2-1)=xdx/(x^2+1)
ln|y^2-1|/2=ln|x^2+1|/2+C
ln|y^2-1|=ln(x^2+1)+C
y^2-1=C(x^2+1)
y^2=C(x^2+1)+1
y=±√(C(x^2+1)+1)