JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 June 2022, Shift 2, Maths Q13

Question 13 of 90 in this shift, Maths question 13 of 30, Section A.

y = y(x)

is the solution of the differential equation

2x^2 \frac{dy}{dx} - 2xy + 3y^2 = 0

such that

y(e) = \frac{e}{3}

, then

y(1)

is equal to

(1) $\frac{1}{3}$
(2) $\frac{2}{3}$ Official answer
(3) $\frac{3}{2}$
(4)3

Official answer

Option 2

NTA final key.

Chapter: Differential Equations
Topic: Homogeneous Equations
Idea tested: Finding Particular Solutions

Same topic in other shifts

All Homogeneous Equations questions

2 Apr 2026, Shift 2 · Q20Let $x = x(y)$ be the solution of the differential equation $2y^2\frac{dx}{dy} - 2xy + x^2 = 0, y > 1, x(e) = e$ . Then $x(e^2)$ is equal to:MediumSingle correct
5 Apr 2026, Shift 1 · Q25Let $y = y(x)$ be the solution of the differential equation…HardNumerical value
6 Apr 2024, Shift 2 · Q13Suppose the solution of the differential equation $\frac{dy}{dx}=\frac{(2+\alpha)x-\beta y+2}{\beta x-2\alpha y-(\beta\gamma-4\alpha)}$ …HardSingle correct
8 Apr 2024, Shift 2 · Q27Let $\alpha|x| = |y|e^{xy-\beta}$ , $\alpha, \beta \in \mathbb{N}$ be the solution of the differential equation…HardNumerical value
9 Apr 2024, Shift 1 · Q10The solution of the differential equation $(x^2+y^2)dx-5xy\,dy=0$ , $y(1)=0$ , is :MediumSingle correct
31 Jan 2024, Shift 1 · Q12The solution curve of the differential equation $y\frac{dx}{dy}=x(\log_ex-\log_ey+1),\ x>0,\ y>0$ passing through the point $(e,1)$ isMediumSingle 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 108 of the 174 JEE Main shifts held from 2017 to 2026.