i'll try to answer this .
x+y=exy.................................(i)
diff wrt x on both sides we get,
1+dy/dx=exy(xdy/dx+y)
dy/dx=(y.exy-1)/( 1-xexy )
FOR the tgt to be to ll to y axis
lim
( 1-xe
xy )

0
1=x.exy ......................................(ii)
by appr graph we get x=1 and y=0
or as x has to be greater than zero and comparing (i) and (ii)
we get x=1 and y=0.
just point out if any mistake if there are so which there are none.