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Saturday, 31 October

JEE Main · Maths · Differential Equations

Alternative Substitution x = vy

JEE Main asked Alternative Substitution x = vy 2 times in 2 of the 108 shifts Lumi analysed, in 2022 and 2024. It belongs to Homogeneous Equations, in Differential Equations (Maths). The longest wait between two years asking it was 2 years.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2022
last in 2024
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2022 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170’200’210.04’220’230.05’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20250 of 8
  • 20241 of 18
  • 20230 of 12
  • 20221 of 24
  • 20210 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

  • Solve initial value differential equation
  • Solve homogeneous ode and evaluate on line

Difficulty

Easy 0Medium 1Hard 1

Every question was multiple choice.

Every question

All 2 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 31 Jan 2024, Shift 1 · Q12The solution curve of the differential equation ydxdy=x(log⁡ex−log⁡ey+1), x>0, y>0y\frac{dx}{dy}=x(\log_ex-\log_ey+1),\ x>0,\ y>0 passing through the point (e,1)(e,1) isMediumSingle correct
  2. 25 Jun 2022, Shift 1 · Q18If the solution curve y=y(x)y=y(x) of the differential equation y2dx+(x2−xy+y2)dy=0y^2\mathrm{d}x+(x^2-xy+y^2)\mathrm{d}y=0, which passes through the point…HardSingle correct

Shifts: 25 Jun 2022, Shift 1, 31 Jan 2024, Shift 1.

Same topic

Other ideas in Homogeneous Equations

Homogeneous Equations has 9 ideas JEE Main has asked; 5 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas