Discussion
The equation \( \dfrac{dy}{dx} = \dfrac{x}{y} \) is solved by
Answer: B
Writing it as \( y\,dy = x\,dx \) puts each variable with its own differential, so
\[ \frac{y^{2}}{2} \;=\; \frac{x^{2}}{2} + C \quad \Longrightarrow \quad y^{2} - x^{2} \;=\; k. \]
The solution curves are rectangular hyperbolae. Separation is always worth trying first, since it needs no auxiliary construction at all
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