Exercise $3($Section $3).$ Prove that the equation $f(x,y)$:$=ylog(y)-xy=0$ defines $y$ as an implicit function of $x,$ making certain to provide all domains of definition. Thus, stating the interval of solution, prove that $f(x,y)=0$ describes an implicit solution of the differential equation

$[6$ marks$]$

$F(x,y,y^{\text{'}})$:$=y\frac{dy}{dx}-y^2=0$