Learn

Saturday, 31 October

JEE Main · Maths · Differential Equations

Exact Differential Recognition in LDEs

JEE Main asked Exact Differential Recognition in LDEs 3 times in 3 of the 108 shifts Lumi analysed, in 2021, 2022 and 2024. It belongs to Linear Differential Equations, in Differential Equations (Maths). The longest wait between two years asking it was 2 years.

Updated 2026-10-24

Times asked
3
in 3 shifts
Years
3 of 8
First asked
2021
last in 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170’200.03’210.04’220’230.05’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 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
  • 20211 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
  • Value from solution of differential equation

Difficulty

Easy 0Medium 2Hard 1

Every question was multiple choice.

Every question

All 3 questions

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

  1. 30 Jan 2024, Shift 1 · Q12Let y=y(x)y=y(x) be the solution of the differential equation sec⁡x dy+{2(1−x)tan⁡x+x(2−x)}dx=0\sec x\,dy+\{2(1-x)\tan x+x(2-x)\}dx=0 such that y(0)=2y(0)=2. Then y(2)y(2) is…MediumSingle correct
  2. 26 Jun 2022, Shift 2 · Q9If y=y(x)y = y(x) is the solution of the differential equation xdydx+2y=xexx\frac{dy}{dx} + 2y = x e^x, y(1)=0y(1) = 0 then the local maximum value of the…HardSingle correct
  3. 27 Aug 2021, Shift 1 · Q71Let us consider a curve, y=f(x)y=f(x) passing through the point (−2,2)(-2, 2) and the slope of the tangent to the curve at any point (x,f(x))(x, f(x))…MediumSingle correct

Shifts: 27 Aug 2021, Shift 1, 26 Jun 2022, Shift 2, 30 Jan 2024, Shift 1.

Same topic

Other ideas in Linear Differential Equations

Linear Differential Equations has 18 ideas JEE Main has asked; 14 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas