SIMON-MARAIS 2018 A3

Let $y(x)$ be the unique solution of the differential equation

$\frac{dy}{dx} = \log_e \frac{y}{x}, \quad \text{where } x > 0 \text{ and } y > 0,$

with the initial condition $y(1) = 2018$ .

How many positive real numbers $x$ satisfy the equation $y(x) = 2000$ ?

A model read this text from the scan of the paper by OCR, with vision/local (GLM-OCR-8bit). No person has checked it against the paper yet.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.