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Saturday, 31 October

JEE Main · Maths · Differential Equations

Direct Integration

JEE Main asked Direct Integration 3 times in 3 of the 108 shifts Lumi analysed, in 2021, 2022 and 2026. It belongs to Variable Separable Form, in Differential Equations (Maths). The longest wait between two years asking it was 4 years.

Updated 2026-10-24

Times asked
3
in 3 shifts
Years
3 of 8
First asked
2021
last in 2026
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200.03’210.04’220’230’240’250.11’26

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: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 1 in 9 shifts.

Shift by shift

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

  • 20261 of 9
  • 20250 of 8
  • 20240 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
  • Differential equation representing a circle

Difficulty

Easy 1Medium 0Hard 2

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. 2 Apr 2026, Shift 1 · Q17If the curve y=f(x)y=f(x) passes through the point (1,e)(1, e) and satisfies the differential equation dy=y(2+log⁡ex) dxdy=y(2+\log_e x)\,dx, x>0x>0, then f(e)f(e)…EasySingle correct
  2. 30 Jun 2022, Shift 1 · Q12Let dydx=ax−by+abx+cy+a\frac{dy}{dx} = \frac{ax - by + a}{bx + cy + a}, a, b, c∈Rc \in \mathbf{R}, represents a circle with center (α,β)(\alpha, \beta). Then,…HardSingle correct
  3. 31 Aug 2021, Shift 2 · Q70If dydx=2xy+2y⋅2x2x+2x+ylog⁡e2\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{2^x y + 2^y \cdot 2^x}{2^x + 2^{x+y}\log_e 2}, y(0)=0y(0) = 0, then for y=1y = 1, the value of xx…HardSingle correct

Shifts: 31 Aug 2021, Shift 2, 30 Jun 2022, Shift 1, 2 Apr 2026, Shift 1.

Same topic

Other ideas in Variable Separable Form

Variable Separable Form has 17 ideas JEE Main has asked; 8 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas