∵dy/dx=(x+y^3)/(xy^2)==>xy^2dy=(x+y^3)dx==>y^2dy/x^3=dx/x^3+y^3dx/x^4 (等式两端同除x^4)==>d(y^3)/(3x^3)+y^3d(1/(3x^3))+d(1/(2x^2))=0==>d(y^3/(3x^3))+d(1/(2x^2))=0==>y^3/(3x^3)+1/(2x^2)=C/6 (C是常数)=...