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Jee Main 2025 — Hard JEE math MCQ

Let $x = x(y)$ be the solution of the differential equation $y^2 \, dx + (x - \frac{1}{y}) \, dy = 0$. If $x
  1. A. = 1$, then $x \left( \frac{1}{3} \right)$ is: (1) $\frac{1}{3} + e$
  2. B. $3 + e$
  3. C. $3 - e$
  4. D. $\frac{3}{2} + e$

Solution

The correct option is **C**. (C. $3 - e$)

MATH

hard • PYQ Reworded
Question
Read carefully, then pick the best option.
Let x=x(y)x = x(y) be the solution of the differential equation y2 dx+(x−1y) dy=0y^2 \, dx + (x - \frac{1}{y}) \, dy = 0. If $x
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