JEE Main Maths · Differential Equations

Substitution y = vx

Substitution y = vx (Differential Equations) was asked 5 times in 5 JEE Main shifts, 2020–2026, out of the 42 shifts Lumi analysed. 1 of the 5 had a numerical answer.

Times asked: 5; in 5 shifts
Years: 2020–2026
Usual format: Single correct; Multi-step
Pattern: Frequent; repeats across shifts

How it is asked

Solve initial value differential equation
Solve initial value differential equation then count circles

Difficulty

Easy 0Medium 4Hard 1

Where it sits

Chapter: Differential Equations. Topic: Homogeneous Equations, 9 questions over 5 ideas.

Every time it came

All 5 questions

Newest first, each with its options and official answer.

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
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