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.


Inspiration.

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