已知函数的全微分df(x,y)=(3x2+4xy-y2+1)dx+(2x2-2xy+3y2-1)dy，则f(x,y)等于（　　）.

[单选题]已知函数的全微分df(x,y)=(3x2+4xy-y2+1)dx+(2x2-2xy+3y2-1)dy，则f(x,y)等于（　　）.A.B.C.D.

[单选题]已知函数的全微分df(x,y)=(3x2+4xy-y2+1)dx+(2x2-2xy+3y2-1)dy，则f(x,y)等于（　　）.A.B.C.D.

(3)(x^2+2xy-y^2)dx+(y^2+2xy-x^2)dy=0,y|_(x=1)=1;(3)$(x^{2}+2xy-y^{2})dx+(y^{2}+2

6.求下列全微分的原函数:-|||-(1) ((x)^2+2xy-(y)^2)dx+((x)^2-2xy-(y)^2)dy-|||-(2) ^x[ e(x-y+

(2)(x^2+2xy-y^2)dx+(y^2+2xy-x^2)dy=0, y|_(x=1)=1.(2)$(x^{2}+2xy-y^{2})dx+(y^{2}+

+2y)dx+(2x+3(y)^2)dy在整个xoy平面内是某一函数+2y)dx+(2x+3(y)^2)dy的全微分，则+2y)dx+(2x+3(y)^2)dy

求微分方程(x^3-y^2)dx+(x^2y+xy)dy=0,的通解。(1)(14分)求微分方程$(x^{3}-y^{2})dx+(x^{2}y+xy)dy=0

微分方程x^2y`+xy= y^2, y|x=1=1 的特解为A x^2y`+xy= y^2, y|x=1=1 B x^2y`+xy= y^2, y|x=1=1

【题目】 (3x+6xy+3(y)^2)dx+(2(x)^2+3xy)dy=0, 解-|||-微分方程。

1.函数 (x+y,xy)=(x)^2+(y)^2-xy, 则 f(x,y)=