(1+x2)dy/dx=1-y2,
dy/(1-y2)=dx/(1+x2) (separation of variables).
1/(1-y2)=A/(1-y)+B/(1+y) (partial fractions).
A+Ay+B-By=1, so A+B=1, A-B=0, A=B=½.
½∫dy/(1-y)+½∫dy/(1+y)=∫dx/(1+x2)=tan-1(x)+C, where C is a constant.
ln((1+y)/(1-y))=2tan-1(x)+K,
(1+y)/(1-y)=e2tan⁻¹(x)+K,
1+y=e2tan⁻¹(x)+K-ye2tan⁻¹(x)+K,
y(1+e2tan⁻¹(x)+K)=e2tan⁻¹(x)+K-1,
y=(e2tan⁻¹(x)+K-1)/(e2tan⁻¹(x)+K+1), where K is a constant.