x(y^2+1)dx+y(1-x^2)dy=0
y/(1+y²)dy=x/(x²-1)dx
即
2y/(1+y²)dy=2x/(x²-1)dx
两边积分,得
ln(1+y²)=ln(x²-1)+lnc
所以
通解为
1+y²=c(x²-1)