设(ay-2xy2)dx+(bx2y+4x+3)dy为某个二元函数的全微分,则a=_______,b=_______.

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问题 设(ay-2xy2)dx+(bx2y+4x+3)dy为某个二元函数的全微分,则a=_______,b=_______.

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答案4,-2

解析 令P(x,y)=ay-2xy2,Q(x,y)=bx2y+4x+3,
因为(ay-2xy2)dx+(bx2y+4x+3)dy为某个二元函数的全微分,

=a-4xy,于是a=4,b=-2.
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