两边对腊消x求导,注意y是关于x的函轮慧知数:
(e^y)'*y'+(xy)'=0
e^y*dx/dy+y+x*dy/dx=0
解得:dy/dx=-y/(e^y+x)
由原碧孙方程得:x=(e-e^y)/y
代入得:dy/dx=-y^2/[(y-1)e^y+e]
注意:最后尽量化为y的形式,不要有x出现.我大一学微积分时老师强调的.
求芹尺导后得e^ydy+ydx+xdy=0，再扮轿同时除以dx，得e^ydy/dx+y+xdy/dx=0,即dy/dx=-y/嫌缺高(e^y+x)
解：对友咐方程两对求导，得
(e^y)*y'+y+xy'型誉=0
整理得y'=-y/(x+e^y)
所以dy/卜告段dx=-y/(x+e^y)
e^y+xy-e=0
d(e^y) + d(xy) - d(e) = 0
e^y dy + xdy + ydx = 0
(e^y + x)dy = -ydx
dy/稿举卖销dx = -y/键配碧(e^y + x)