JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 July 2021, Shift 2, Maths Q67

Question 67 of 90 in this shift, Maths question 7 of 30, Section A.

Let

y=y(x)

be the solution of the differential equation

x\,dy=(y+x^3\cos x)\,dx

with

y(\pi)=0

, then

y\left(\frac{\pi}{2}\right)

is equal to :

(1) $\frac{\pi^2}{2}+\frac{\pi}{4}$
(2) $\frac{\pi^2}{4}-\frac{\pi}{2}$
(3) $\frac{\pi^2}{2}-\frac{\pi}{4}$
(4) $\frac{\pi^2}{4}+\frac{\pi}{2}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Particular Solution Solving

Same idea in other shifts

Asked 11× in all

5 Apr 2026, Shift 2 · Q25Let $y=y(x)$ be the solution of the differential equation $(\tan x)^{1/2}\,dy=\left(\sec^3 x-(\tan x)^{3/2}\,y\right)dx$ ,…HardNumerical value
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
4 Apr 2024, Shift 1 · Q26Let the solution $y=y(x)$ of the differential equation $\frac{dy}{dx}-y=1+4\sin x$ satisfy $y(\pi)=1$ . Then…MediumNumerical value
26 Jul 2022, Shift 1 · Q11If $\frac{dy}{dx} + 2y \tan x = \sin x$ , $0 < x < \frac{\pi}{2}$ and $y\left(\frac{\pi}{3}\right) = 0$ , then the maximum value of $y(x)$ …MediumSingle correct
26 Jul 2022, Shift 2 · Q10Let the solution curve $y=f(x)$ of the differential equation $\frac{dy}{dx}+\frac{xy}{x^2-1}=\frac{x^4+2x}{\sqrt{1-x^2}}$ , $x\in(-1,1)$ …HardSingle correct
27 Jul 2022, Shift 1 · Q25Let $y = y(x)$ be the solution curve of the differential equation…HardNumerical value
29 Jul 2022, Shift 2 · Q10Let $y=y(x)$ be the solution curve of the differential equation…HardSingle correct
26 Jun 2022, Shift 1 · Q25Let the solution curve $y = y(x)$ of the differential equation $(4 + x^2)\,dy - 2x(x^2 + 3y + 4)\,dx = 0$ pass through the origin. Then…MediumNumerical value

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 108 of the 174 JEE Main shifts held from 2017 to 2026.