The solution curve y = y(x) of the differential equation (1 + y²)… | JEE Main 2024 Mathematics PYQ

MCQMediumJEE Main 2024 · 29 January, Shift 1Separation of Variables

The solution curve $y = y(x)$ of the differential equation $(1 + y^2)(1 + \log(x)) \, dx + x \, dy = 0$ , $x > 0$ , passes through the point $(1, 1)$ . If $y(e) = \frac{\alpha - \tan\left(\frac{3}{2}\right)}{\beta + \tan\left(\frac{3}{2}\right)}$ , then $\alpha + 2\beta$ is:

A
$2$
B
$3$
C
$1$
D
$4$

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