JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 25 July 2022, Shift 1, Maths Q11

Question 11 of 90 in this shift, Maths question 11 of 30, Section A.

The general solution of the differential equation

(x-y^2)\,dx+y(5x+y^2)\,dy=0

is :

(1) $(y^2+x)^4=\mathrm{C}\,|(y^2+2x)^3|$ Official answer
(2) $(y^2+2x)^4=\mathrm{C}\,|(y^2+x)^3|$
(3) $|(y^2+x)^3|=\mathrm{C}\,(2y^2+x)^4$
(4) $|(y^2+2x)^3|=\mathrm{C}\,(2y^2+x)^4$

Official answer

Option 1

NTA final key (2022 Session 2).

Chapter: Differential Equations
Topic: Homogeneous Equations
Idea tested: Identifying Equations Reducible to Homogeneous Form

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
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
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

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.