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Saturday, 31 October

JEE Main · Maths · Differential Equations

Generalized Substitution for LDEs

JEE Main asked Generalized Substitution for LDEs 6 times in 6 of the 108 shifts Lumi analysed, in 2021, 2023, 2024 and 2025. It belongs to Linear Differential Equations, in Differential Equations (Maths). The longest wait between two years asking it was 2 years. In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
6
in 6 shifts
Years
4 of 8
First asked
2021
last in 2025
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2023, 2024 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.10’210’220.07’230.05’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 3 in 24 shifts · 2022: 0 in 24 shifts · 2023: 1 in 12 shifts · 2024: 1 in 18 shifts · 2025: 1 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
  • 20251 of 8
  • 20241 of 18
  • 20231 of 12
  • 20220 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
  • De reducible to linear

Difficulty

Easy 0Medium 3Hard 3

2 of the 6 questions had a numerical answer.

Every question

All 6 questions

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

  1. 4 Apr 2025, Shift 2 · Q20If a curve y=y(x)y=y(x) passes through the point (1,π2)\left(1,\frac{\pi}{2}\right) and satisfies the differential equation…HardSingle correct
  2. 8 Apr 2024, Shift 2 · Q13Let y=y(x)y = y(x) be the solution curve of the differential equation sec⁡ydydx+2xsin⁡y=x3cos⁡y\sec y \frac{dy}{dx} + 2x\sin y = x^3\cos y, y(1)=0y(1) = 0. Then…MediumSingle correct
  3. 6 Apr 2023, Shift 2 · Q12If the solution curve f(x,y)=0f(x,y)=0 of the differential equation (1+log⁡ex)dxdy−xlog⁡ex=ey, x>0\left(1+\log_e x\right)\frac{dx}{dy}-x\log_e x=e^y,\ x>0, passes through…HardSingle correct
  4. 25 Jul 2021, Shift 1 · Q85Let y=y(x)y=y(x) be solution of the following differential equation eydydx−2eysin⁡x+sin⁡xcos⁡2x=0e^y\frac{dy}{dx}-2e^y\sin x+\sin x\cos^2x=0,…MediumNumerical value
  5. 26 Feb 2021, Shift 1 · Q84If y=y(x)y=y(x) is the solution of the equation esin⁡ycos⁡y dydx+esin⁡ycos⁡x=cos⁡xe^{\sin y}\cos y\,\frac{dy}{dx}+e^{\sin y}\cos x=\cos x, y(0)=0y(0)=0; then…MediumNumerical value
  6. 26 Aug 2021, Shift 2 · Q68Let y(x)y(x) be the solution of the differential equation 2x2 dy+(ey−2x)dx=02x^2\,\mathrm{d}y+(\mathrm{e}^y-2x)\mathrm{d}x=0, x>0x>0. If y(e)=1y(\mathrm{e})=1,…HardSingle correct

Shifts: 26 Feb 2021, Shift 1, 25 Jul 2021, Shift 1, 26 Aug 2021, Shift 2, 6 Apr 2023, Shift 2, 8 Apr 2024, Shift 2, 4 Apr 2025, 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