# Inspired by Arkajyoti Banerjee

Calculus Level 5

How many differentiable functions $$f: \mathbb{R} \rightarrow \mathbb{R}$$ are there such that $$f(0) = 0$$ and

$y \frac{dy}{dx} = 2xy ?$

Note: It is intentional that $$y$$ appears on both sides of the equation. Cancel at your own risk.

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