JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 29 June 2022, Shift 1, Maths Q22

Question 22 of 90 in this shift, Maths question 22 of 30, Section B.

Let

y = y(x)

be the solution of the differential equation

\frac{dy}{dx} + \frac{\sqrt{2}y}{2\cos^4 x - \cos 2x} = xe^{\tan^{-1}(\sqrt{2}\cot 2x)}

0 < x < \frac{\pi}{2}

with

y\left(\frac{\pi}{4}\right) = \frac{\pi^2}{32}

. If

y\left(\frac{\pi}{3}\right) = \frac{\pi^2}{18}e^{-\tan^{-1}(\alpha)}

, then the value of

3\alpha^2

is equal to ____________.

Official answer

NTA final key (2022 Session 1).

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Inverse Trigonometric Integrating Factors

Same topic in other shifts

All Linear Differential Equations questions

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8 Apr 2026, Shift 2 · Q17Let $y = y(x)$ be the solution of the differential equation $x\sqrt{1-x^2}\,dy + \left(y\sqrt{1-x^2} - x\cos^{-1}x\right)dx = 0$ ,…MediumSingle 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.