The curve through $(2,2)$ satisfies $(x+y)\dfrac{\mathrm{d}y}{\mathrm{d}x}=y$ for $x0$ and \(

Question

The curve through $(2,2)$ satisfies $(x+y)\dfrac{\mathrm{d}y}{\mathrm{d}x}=y$ for $x>0$ and $y>0$. Find an implicit equation for the curve.

Accepted Answer

$y\left(1+\ln\dfrac{y}{2}\right)=x$

Implicit logarithmic curve through (2, 2)