已知du(x,y)=[axy3+cos(x+2y)]dx+[3x2y2+bcos(x+2y)]dy,则( )

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问题 已知du(x,y)=[axy3+cos(x+2y)]dx+[3x2y2+bcos(x+2y)]dy,则(    )

选项 A、a=2,b=一2.
B、a=3,b=2.
C、a=2,b=2.
D、a=一2,b=2.

答案C

解析 由du(x,y)=(axy3+cos(x+2y))dx+(3x2y2+σcos(x+2y))dy知

  即3axy2一2sin(x+2y)≡6xy2一bsin(x+2y),则a=2,b=2,故选C.
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