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Saturday, 31 October

JEE Main · Maths · Differential Equations

Substitution y = vx

JEE Main asked Substitution y = vx 10 times in 10 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023, 2024 and 2026. It belongs to Homogeneous Equations, in Differential Equations (Maths). The longest wait between two years asking it was 2 years. In 2020 and 2022 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
10
in 10 shifts
Years
6 of 8
First asked
2020
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022, 2023, 2024 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170.17’200.03’210.14’220.07’230.05’240’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 2 in 12 shifts · 2021: 1 in 24 shifts · 2022: 4 in 24 shifts · 2023: 1 in 12 shifts · 2024: 1 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
  • 20241 of 18
  • 20231 of 12
  • 20224 of 24
  • 20211 of 24
  • 20202 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
  • Solve initial value differential equation then count circles

Difficulty

Easy 0Medium 7Hard 3

3 of the 10 questions had a numerical answer.

Every question

All 10 questions

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

  1. 5 Apr 2026, Shift 1 · Q25Let y=y(x)y = y(x) be the solution of the differential equation…HardNumerical value
  2. 9 Apr 2024, Shift 1 · Q10The solution of the differential equation (x2+y2)dx−5xy dy=0(x^2+y^2)dx-5xy\,dy=0, y(1)=0y(1)=0, is :MediumSingle correct
  3. 10 Apr 2023, Shift 1 · Q10The slope of tangent at any point (x,y)(x,y) on a curve y=y(x)y=y(x) is x2+y22xy\frac{x^2+y^2}{2xy}, x>0x>0. If y(2)=0y(2)=0, then a value of y(8)y(8) isMediumSingle correct
  4. 29 Jun 2022, Shift 1 · Q2Let the solution curve of the differential equation xdydx−y=y2+16x2x\frac{dy}{dx} - y = \sqrt{y^2 + 16x^2}, y(1)=3y(1) = 3 be y=y(x)y = y(x). Then y(2)y(2) is…MediumSingle correct
  5. 28 Jun 2022, Shift 1 · Q10Let the solution curve y=y(x)y=y(x) of the differential equation…HardSingle correct
  6. 28 Jul 2022, Shift 1 · Q1Let the solution curve of the differential equation x dy=(x2+y2+y)dx, x>0x\,dy=\left(\sqrt{x^2+y^2}+y\right)dx,\ x>0, intersect the line x=1x=1 at y=0y=0 and…MediumSingle correct
  7. 25 Jul 2022, Shift 2 · Q25Let y=y(x)y=y(x) be the solution of the differential equation dydx=4y3+2yx23xy2+x3, y(1)=1\frac{dy}{dx}=\frac{4y^3+2yx^2}{3xy^2+x^3},\ y(1)=1. If for some…MediumNumerical value
  8. 18 Mar 2021, Shift 2 · Q86Let y=y(x)y=y(x) be the solution of the differential equation x dy−y dx=(x2−y2) dxx\,dy-y\,dx=\sqrt{(x^2-y^2)}\,dx, x≥1x\ge1, with y(1)=0y(1)=0. If the area bounded…HardNumerical value
  9. 2 Sep 2020, Shift 2 · Q63If a curve y=f(x)y=f(x), passing through the point (1, 2)(1,\,2), is the solution of the differential equation, 2x2 dy=(2xy+y2) dx2x^2\,dy=(2xy+y^2)\,dx, then…MediumSingle correct
  10. 9 Jan 2020, Shift 2 · Q64If dydx=xyx2+y2\frac{dy}{dx}=\frac{xy}{x^2+y^2}; y(1)=1y(1)=1; then a value of xx satisfying y(x)=ey(x)=e is :MediumSingle correct

Shifts: 9 Jan 2020, Shift 2, 2 Sep 2020, Shift 2, 18 Mar 2021, Shift 2, 28 Jun 2022, Shift 1, 29 Jun 2022, Shift 1, 25 Jul 2022, Shift 2, 28 Jul 2022, Shift 1, 10 Apr 2023, Shift 1, 9 Apr 2024, Shift 1, 5 Apr 2026, Shift 1.

Same topic

Other ideas in Homogeneous Equations

Homogeneous Equations has 9 ideas JEE Main has asked; 5 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas