JEE Main Maths · Differential Equations

Homogeneous Equations in JEE Main

Name: Homogeneous Equations: JEE Main previous year questions
Creator: Lumi

Homogeneous Equations (Maths, Differential Equations) came 9 times in 9 of the 42 JEE Main shifts Lumi analysed, across 5 distinct ideas. 5 of them came in 2024–26; it was last asked in 2026.

Questions: 9; in 9 shifts
Ideas asked: 5; 1 asked more than once
Numerical answer: 1; 11% of its questions
Pattern: Frequent; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 0Medium 6Hard 3

Format

Single correct8 Q
Numerical value1 Q

Ideas inside the topic

5 ideas

Substitution y = vx5 Q
Identifying Homogeneous Functions1 Q
Identifying Equations Reducible to Homogeneous Form1 Q
Shift of Origin Method for Reducible Equations1 Q
Alternative Substitution x = vy1 Q

Where it sits

Part of Differential Equations, which had 57 questions in all. Homogeneous Equations accounts for 16% of them. In Lumi's JEE taxonomy it belongs to Calculus.

Every question

All 9 Homogeneous Equations questions

Newest first, each with its options and official answer.

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
25 Jul 2022, Shift 1 · Q11The general solution of the differential equation $(x-y^2)\,dx+y(5x+y^2)\,dy=0$ is :HardSingle 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
29 Jun 2022, Shift 1 · Q2Let the solution curve of the differential equation $x\frac{dy}{dx} - y = \sqrt{y^2 + 16x^2}$ , $y(1) = 3$ be $y = y(x)$ . Then $y(2)$ is…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