利用曲线积分,求微分表达式的原函数 (x^2+2xy-y^2)dx+(x^2-2xy-y^2)dy

(x^2+2xy-y^2)dx+(x^2-2xy-y^2)dyP=(x^2+2xy-y^2)Q=(x^2-2xy-y^2)Py=Qx,积分与路径无关z(x,y)=∫(x^2+2xy-y^2)dx+(x^2-2xy-y^2)dy=x^3/3-y^3/3+∫(2xydx+x^2dy)-∫(y^2dx+2xydy=x^3/3-y^3/3+x^2y-y^2x+C