JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 29 June 2022, Shift 1, Maths Q2

Question 2 of 90 in this shift, Maths question 2 of 30, Section A.

Let the solution curve of the differential equation

x\frac{dy}{dx} - y = \sqrt{y^2 + 16x^2}

y(1) = 3

y = y(x)

. Then

y(2)

is equal to :

(1)15Official answer
(2)11
(3)13
(4)17

Official answer

Option 1

NTA final key (2022 Session 1).

Chapter: Differential Equations
Topic: Homogeneous Equations
Idea tested: Substitution y = vx

Same idea in other shifts

Asked 5× in all

5 Apr 2026, Shift 1 · Q25Let $y = y(x)$ 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
28 Jul 2022, Shift 1 · Q1Let the solution curve of the differential equation $x\,dy=\left(\sqrt{x^2+y^2}+y\right)dx,\ x>0$ , intersect the line $x=1$ at $y=0$ and…MediumSingle correct
9 Jan 2020, Shift 2 · Q64If $\frac{dy}{dx}=\frac{xy}{x^2+y^2}$ ; $y(1)=1$ ; then a value of $x$ satisfying $y(x)=e$ is :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.