同时除以xy, 则(y+1/y)dx+(1/x-x)dy则dx/((1/x-x))=-dy/(y+1/y)两边同时各自积分dx/((1/x-x))=-dy/(y+1/y)xdx/((1-x^2)=-ydy/(y^2+1)-1/2ln(1-x^2)=-1/2ln(y^2+1)+c1则ln(1-x^2)=ln(y^2+1)+lnc2则1-x^2=Cy^2+C即：x^2+Cy^2+C=1
