Thomas' Calculus 13th Edition

$-\ln2-1$
$2xy+e^{x+y}-2=0$ $2ydx+2xdy+e^{x+y}dx+e^{x+y}dy=0$ $2\ln2dx+e^{\ln2}dx+e^{\ln2}dy=0$ when $x=0,y=\ln2$ $2\ln2dx+2dx+2dy=0$ $2dy=-(2\ln2+2)dx$ $\frac{dy}{dx}=-(\ln2+1)$