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Saturday, 31 October

JEE Main · Maths · Differential Equations

Particular Solution Solving

JEE Main asked Particular Solution Solving 11 times in 11 of the 108 shifts Lumi analysed, in 2021, 2022, 2024 and 2026. It belongs to Linear Differential Equations, in Differential Equations (Maths). The longest wait between two years asking it was 2 years. In 2021, 2022 and 2026 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
11
in 11 shifts
Years
4 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, 2024 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170’200.10’210.18’220’230.05’240’250.22’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 3 in 24 shifts · 2022: 5 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 in 18 shifts · 2025: 0 in 8 shifts · 2026: 2 in 9 shifts.

Shift by shift

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

  • 20262 of 9
  • 20250 of 8
  • 20241 of 18
  • 20230 of 12
  • 20225 of 24
  • 20213 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
  • Particular solution of linear de

Difficulty

Easy 0Medium 7Hard 4

4 of the 11 questions had a numerical answer.

Every question

All 11 questions

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

  1. 8 Apr 2026, Shift 2 · Q17Let y=y(x)y = y(x) be the solution of the differential equation x1−x2 dy+(y1−x2−xcos⁡−1x)dx=0x\sqrt{1-x^2}\,dy + \left(y\sqrt{1-x^2} - x\cos^{-1}x\right)dx = 0,…MediumSingle correct
  2. 5 Apr 2026, Shift 2 · Q25Let y=y(x)y=y(x) be the solution of the differential equation (tan⁡x)1/2 dy=(sec⁡3x−(tan⁡x)3/2 y)dx(\tan x)^{1/2}\,dy=\left(\sec^3 x-(\tan x)^{3/2}\,y\right)dx,…HardNumerical value
  3. 4 Apr 2024, Shift 1 · Q26Let the solution y=y(x)y=y(x) of the differential equation dydx−y=1+4sin⁡x\frac{dy}{dx}-y=1+4\sin x satisfy y(π)=1y(\pi)=1. Then…MediumNumerical value
  4. 26 Jun 2022, Shift 1 · Q25Let the solution curve y=y(x)y = y(x) of the differential equation (4+x2) dy−2x(x2+3y+4) dx=0(4 + x^2)\,dy - 2x(x^2 + 3y + 4)\,dx = 0 pass through the origin. Then…MediumNumerical value
  5. 29 Jul 2022, Shift 2 · Q10Let y=y(x)y=y(x) be the solution curve of the differential equation…HardSingle correct
  6. 27 Jul 2022, Shift 1 · Q25Let y=y(x)y = y(x) be the solution curve of the differential equation…HardNumerical value
  7. 26 Jul 2022, Shift 2 · Q10Let the solution curve y=f(x)y=f(x) of the differential equation dydx+xyx2−1=x4+2x1−x2\frac{dy}{dx}+\frac{xy}{x^2-1}=\frac{x^4+2x}{\sqrt{1-x^2}}, x∈(−1,1)x\in(-1,1)…HardSingle correct
  8. 26 Jul 2022, Shift 1 · Q11If dydx+2ytan⁡x=sin⁡x\frac{dy}{dx} + 2y \tan x = \sin x, 0<x<π20 < x < \frac{\pi}{2} and y(π3)=0y\left(\frac{\pi}{3}\right) = 0, then the maximum value of y(x)y(x)…MediumSingle correct
  9. 16 Mar 2021, Shift 2 · Q68If y=y(x)y=y(x) is the solution of the differential equation dydx+(tan⁡x) y=sin⁡x\frac{dy}{dx}+(\tan x)\,y=\sin x, 0≤x≤π30\le x\le\frac{\pi}{3}, with y(0)=0y(0)=0, then…MediumSingle correct
  10. 25 Jul 2021, Shift 2 · Q67Let y=y(x)y=y(x) be the solution of the differential equation x dy=(y+x3cos⁡x) dxx\,dy=(y+x^3\cos x)\,dx with y(π)=0y(\pi)=0, then y(π2)y\left(\frac{\pi}{2}\right) is…MediumSingle correct
  11. 22 Jul 2021, Shift 2 · Q70Let y=y(x)y=y(x) be the solution of the differential equation cosec2x dy+2dx=(1+ycos⁡2x) cosec2x dx\mathrm{cosec}^2x\,dy+2dx=(1+y\cos2x)\,\mathrm{cosec}^2x\,dx, with…MediumSingle correct

Shifts: 16 Mar 2021, Shift 2, 22 Jul 2021, Shift 2, 25 Jul 2021, Shift 2, 26 Jun 2022, Shift 1, 26 Jul 2022, Shift 2, 26 Jul 2022, Shift 1, 27 Jul 2022, Shift 1, 29 Jul 2022, Shift 2, 4 Apr 2024, Shift 1, 5 Apr 2026, Shift 2, 8 Apr 2026, Shift 2.

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