验证(x^2-2xy+y^2)dx-(x^2-2xy-y^2)dy是某个二元函数u=u(x,y)的全微分,并求u=u(x,y)

验证(x^2-2xy+y^2)dx-(x^2-2xy-y^2)dy是某个二元函数u=u(x,y)的全微分,并求u=u(x,y) y/x=ln(xy) 求dy/dx(xy-y^2)/(xy+x^2) 求解微分方程 x^2*dy/dx=xy-y^2 求齐次微分方程dy/dx=y^2/xy-x^2 dy/dx=xy/x^2-y^2 dy/dx=1+x+y^2+xy^2 求通解:(xy-x^2)dy=y^2dx 微分方程求解 (x^2y^3+xy)dy=dx 解微分方程 (x^2y^3+xy)dy=dx x^2+xy+y^3=1,求dy/dx dy/dx=(x+y^3)/(xy^2) 微分方程求解 (x^2y^3+xy)dy=dx dy/dx=(x+y^3)/xy^2 常微分方程dy/dx=(x^3+xy^2)/y dy/dx=y^2/(x-xy)是齐次方程吗 1.dy/dx=(y-x)/(y+x)2.x^2*dy/dx=xy-y^2 dx/(x^2-xy+y^2)=dy/(2y^2-xy)的微分方程 （2x+xy^2）dx+（2y+x^2*y）dy=0