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JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 13 April 2023, Shift 2, Maths Q27

Question 27 of 90 in this shift, Maths question 27 of 30, Section B.

If

y=y(x)

is the solution of the differential equation

\frac{dy}{dx}+\frac{4x}{(x^2-1)}y=\frac{x+2}{(x^2-1)^{\frac{5}{2}}}

,

x>1

such that

y(2)=\frac{2}{9}\log_e\left(2+\sqrt{3}\right)

and

y(\sqrt{2})=\alpha\log_e\left(\sqrt{\alpha}+\beta\right)+\beta-\sqrt{\gamma}

,

\alpha,\beta,\gamma\in\mathbb{N}

, then

\alpha\beta\gamma

is equal to ______

Official answer

6

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Integrating Factor Calculation

Same idea in other shifts

Asked 3× in all

4 Apr 2026, Shift 2 · Q19Let $y=y(x)$ be the solution of the differential equation:…HardSingle correct
3 Apr 2025, Shift 1 · Q20Let $g$ be a differentiable function such that $\int_0^x g(t)\,dt = x - \int_0^x t\,g(t)\,dt$ , $x \ge 0$ and let $y = y(x)$ satisfy the…HardSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.