设z=1/y³,则dz/dx=(-3/y^4)(dy/dx) ==>dy/dx=(-y^4/3)(dz/dx)代入原方程,得(-y^4/3)(dz/dx)+2xy+xy^4=0==>dz/dx-6x/y³-3x=0==>dz/dx-6xz-3x=0==>dz/dx=3x(2z+1)==>2dz/(2z+1)=6xdx==>ln│2z+1│=3x²+...