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Saturday, 31 October

JEE Main · Maths · Differential Equations

Linear in x Form

JEE Main asked Linear in x Form 6 times in 6 of the 108 shifts Lumi analysed, in 2021, 2022, 2023 and 2024. It belongs to Linear Differential Equations, in Differential Equations (Maths). The longest wait between two years asking it was 1 year. In 2021 and 2023 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 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022, 2023 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.07’210.04’220.14’230.05’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 2 in 24 shifts · 2022: 1 in 24 shifts · 2023: 2 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
  • 20232 of 12
  • 20221 of 24
  • 20212 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: multi-step.

  • Solve initial value differential equation
  • Solve linear de in x

Difficulty

Easy 0Medium 4Hard 2

3 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. 1 Feb 2024, Shift 2 · Q27If dxdy=1+x−y2y\frac{dx}{dy}=\frac{1+x-y^2}{y}, x(1)=1x(1)=1, then 5x(2)5x(2) is equal to ________.MediumNumerical value
  2. 15 Apr 2023, Shift 1 · Q11Let x=x(y)x=x(y) be the solution of the differential equation 2(y+2)log⁡e(y+2)dx+(x+4−2log⁡e(y+2))dy=02(y+2)\log_e(y+2)dx+\left(x+4-2\log_e(y+2)\right)dy=0, y>−1y>-1 with…HardSingle correct
  3. 8 Apr 2023, Shift 2 · Q28Let the solution curve x=x(y)x = x(y), 0<y<π20 < y < \frac{\pi}{2}, of the differential equation…HardNumerical value
  4. 24 Jun 2022, Shift 1 · Q14If x=x(y)x=x(y) is the solution of the differential equation ydxdy=2x+y3(y+1)ey, x(1)=0y\frac{dx}{dy}=2x+y^3(y+1)e^y,\ x(1)=0; then x(e)x(e) is equal to :MediumSingle correct
  5. 27 Aug 2021, Shift 2 · Q73If the solution curve of the differential equation (2x−10y3)dy+y dx=0(2x - 10y^3)dy + y\,dx = 0, passes through the points (0,1)(0, 1) and (2,β)(2, \beta), then…MediumSingle correct
  6. 3 Aug 2021, Shift 2 · Q87If the solution y=y(x)y = y(x) of the differential equation (y+3x4)dxdy=x, x>0\left(y + 3x^4\right)\frac{dx}{dy} = x,\ x > 0, satisfies y(1)=−1y(1) = -1, then the…MediumNumerical value

Shifts: 3 Aug 2021, Shift 2, 27 Aug 2021, Shift 2, 24 Jun 2022, Shift 1, 8 Apr 2023, Shift 2, 15 Apr 2023, Shift 1, 1 Feb 2024, 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