Consider the differential equation dy/dx = x/y - HSC - SSCE Mathematics Extension 1 - Question 4 - 2021 - Paper 1

Rearranging the equation gives:

$y \, dy = x \, dx.$

Integrating both sides results in:

$\int y \, dy = \int x \, dx$

This yields:

$\frac{y^2}{2} = \frac{x^2}{2} + C,$

where C is the constant of integration.

Multiplying through by 2 results in:

$y^2 = x^2 + 2C,$

which is consistent with option A: y² = x² + c.