已知(axy3-y2cosx)dx+(1+bysinx+3x2y2)dy为某个二元函数f(x,y)的全微分,则a=_,b=_.

问题描述:

已知(axy3-y2cosx)dx+(1+bysinx+3x2y2)dy为某个二元函数f(x,y)的全微分,则a=______,b=______.

由(axy3-y2cosx)dx+(1+bysinx+3x2y2)dy,知P=axy3-y2cosx,Q=1+bysinx+3x2y2而Pdx+Qdy为某个二元函数f(x,y)的全微分,因此Py=Qx即3axy2-2ycosx=6xy2+bycosx比较两边的同类项,得3a=6−2=b即:a=2,b=-2...