直接分离变量即可：dy/dx=(1+y^2)/[xy(1+x^2)]ydy/(1+y^2)=dx/[x(1+x^2)]1/2*d(1+y^2)/(1+y^2)=dx[1/x-x/(1+x^2)]d(1+y^2)/(1+y^2)=2dx/x-2xdx/(1+x^2)d(1+y^2)/(1+y^2)=2dx/x-d(1+x^2)/(1+x^2)积分：ln(1+y^2)=2ln|...
可分离变量的微分方程 是做变量代换 令u=xy吗?
直接分离变量即可：dy/dx=(1+y^2)/[xy(1+x^2)]ydy/(1+y^2)=dx/[x(1+x^2)]1/2*d(1+y^2)/(1+y^2)=dx[1/x-x/(1+x^2)]d(1+y^2)/(1+y^2)=2dx/x-2xdx/(1+x^2)d(1+y^2)/(1+y^2)=2dx/x-d(1+x^2)/(1+x^2)积分：ln(1+y^2)=2ln|...