Question

高数第11题。。。

Answer 1

x=0则y=0+1=1
dy=dx+e^(xy)*d(xy)
=dx+e^(xy)*(xdy+ydx)
=dx+xe^(xy)dy+ye^(xy)dx
所以dy/dx=[1+ye^(xy)]/[1-xe^(xy)]
所以原式=2

Answer 2

当x=0时，y=0+e^0=1
y`=1+(y+xy`)e^xy=1+ye^xy+xy`e^xy
(1-xe^xy)y`=1+ye^xy
y`=(1+ye^xy)/(1-xe^xy)
即dy/dx=(1+ye^xy)/(1-xe^xy)=(1+1)/(1-0)=2 (这一步是直接把x=0，y=1代入得到的)