(1+y^2)dx-(1+x^2)dy=0的通解
问题描述：
(1+y^2)dx-(1+x^2)dy=0的通解
答
(1+y^2)dx-(1+x^2)dy=0
(1+y^2)dx=(1+x^2)dy
1/(1+x^2)dx=1/(1+y^2)dy
arctanx=arctany+c
答
(1+y^2)dx-(1+x^2)dy=0
(1+y^2)dx=(1+x^2)dy
dx/(1+x^2)=dy/(1+y^2)
两边积分
arctanx=arctany+C