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Saturday, 31 October

JEE Main · Maths · Differential Equations

Integrating Factors with Trigonometric Functions

JEE Main asked Integrating Factors with Trigonometric Functions 7 times in 7 of the 108 shifts Lumi analysed, in 2022, 2024, 2025 and 2026. It belongs to Linear Differential Equations, in Differential Equations (Maths). The longest wait between two years asking it was 2 years. In 2022, 2024 and 2025 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
7
in 7 shifts
Years
4 of 8
First asked
2022
last in 2026
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2022, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170’200’210.07’220’230.09’240.25’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 2 in 24 shifts · 2023: 0 in 12 shifts · 2024: 2 in 18 shifts · 2025: 2 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
  • 20252 of 8
  • 20242 of 18
  • 20230 of 12
  • 20222 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

Difficulty

Easy 0Medium 4Hard 3

2 of the 7 questions had a numerical answer.

Every question

All 7 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 · Q20Let y=y(x)y=y(x) be the solution curve of the differential equation (1+sin⁡x)dydx+(y+1)cos⁡x=0(1+\sin x)\frac{dy}{dx}+(y+1)\cos x=0, y(0)=0y(0)=0. If the curve y=y(x)y=y(x)…MediumSingle correct
  2. 3 Apr 2025, Shift 2 · Q20Let y=y(x)y = y(x) be the solution of the differential equation…MediumSingle correct
  3. 2 Apr 2025, Shift 2 · Q25Let y=y(x)y = y(x) be the solution of the differential equation…MediumNumerical value
  4. 31 Jan 2024, Shift 1 · Q11Let y=y(x)y=y(x) be the solution of the differential equation…HardSingle correct
  5. 29 Jan 2024, Shift 1 · Q13A function y=f(x)y=f(x) satisfies f(x)sin⁡2x+sin⁡x−(1+cos⁡2x)f′(x)=0f(x)\sin 2x+\sin x-(1+\cos^2x)f'(x)=0 with condition f(0)=0f(0)=0. Then, f(π2)f\left(\frac{\pi}{2}\right) is…MediumSingle correct
  6. 27 Jun 2022, Shift 2 · Q28Let y=y(x)y=y(x) be the solution of the differential equation (1−x2)dy=(xy+(x3+2)1−x2)dx\left(1-x^2\right)dy=\left(xy+\left(x^3+2\right)\sqrt{1-x^2}\right)dx,…HardNumerical value
  7. 28 Jul 2022, Shift 1 · Q10If y=y(x), x∈(0,π/2)y=y(x),\ x\in(0,\pi/2) be the solution curve of the differential equation…HardSingle correct

Shifts: 27 Jun 2022, Shift 2, 28 Jul 2022, Shift 1, 29 Jan 2024, Shift 1, 31 Jan 2024, Shift 1, 2 Apr 2025, Shift 2, 3 Apr 2025, Shift 2, 2 Apr 2026, 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