Consider the following differential equation.

$(y-x)y^{\text{'}}=y+x$

Let $f(x,y)=\frac{y+x}{y-x}.$ Find the derivative $off.$

$\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}=$

Determine a region $of$ the $xy{x}_0,y_{0}xy-$plane except $at$ the origin.

There $is$ a unique solution $in$ the entire $xy-$plane.

There $is$ a unique solution $in$ any region where $x=y.$

There $is$ a unique solution $in$ any region where $x=0.$

There $is$ a unique solution $in$ any region where $y>xyor$ where $y>x.$