验证下列P(x,y)dx+Q(x,y)dy在整个xOy平面内是某一函数u(x,y)的全微分,并求一个这样的u(x,y): (1)(x+2y)dx+(2x+y)dy; (2)(6xy+2y2)dx+(3x2+4xy)dy; (3)(3x2y+xex)dx+(

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问题 验证下列P(x,y)dx+Q(x,y)dy在整个xOy平面内是某一函数u(x,y)的全微分,并求一个这样的u(x,y):
(1)(x+2y)dx+(2x+y)dy;
(2)(6xy+2y2)dx+(3x2+4xy)dy;
(3)(3x2y+xex)dx+(x3-ysiny)dy.

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