Learn

Saturday, 31 October

JEE Main · Maths · Differential Equations

Integrating Factor Calculation

JEE Main asked Integrating Factor Calculation 22 times in 21 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023, 2024, 2025 and 2026. It belongs to Linear Differential Equations, in Differential Equations (Maths). The longest wait between two years asking it was 1 year. In 2020, 2021, 2022, 2023 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
22
in 21 shifts
Years
7 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, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.20.40’170.17’200.10’210.14’220.35’230.28’240.13’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 2 in 12 shifts · 2021: 3 in 24 shifts · 2022: 4 in 24 shifts · 2023: 5 in 12 shifts · 2024: 6 in 18 shifts · 2025: 1 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
  • 20251 of 8
  • 202425 of 18
  • 20235 of 12
  • 20224 of 24
  • 20213 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
  • Value from linear differential equation solution

Difficulty

Easy 0Medium 7Hard 15

8 of the 22 questions had a numerical answer.

Every question

All 22 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 2026, Shift 2 · Q19Let y=y(x)y=y(x) be the solution of the differential equation:…HardSingle correct
  2. 3 Apr 2025, Shift 1 · Q20Let gg be a differentiable function such that ∫0xg(t) dt=x−∫0xt g(t) dt\int_0^x g(t)\,dt = x - \int_0^x t\,g(t)\,dt, x≥0x \ge 0 and let y=y(x)y = y(x) satisfy the…HardSingle correct
  3. 30 Jan 2024, Shift 1 · Q26Let y=y(x)y=y(x) be the solution of the differential equation (1−x2)dy=[xy+(x3+2)3(1−x2)]dx(1-x^2)dy=\left[xy+(x^3+2)\sqrt{3(1-x^2)}\right]dx, −1<x<1-1<x<1, y(0)=0y(0)=0. If…MediumNumerical value
  4. 1 Feb 2024, Shift 1 · Q28If x=x(t)x=x(t) is the solution of the differential equation (t+1)dx=(2x+(t+1)4)dt(t+1)dx=(2x+(t+1)^4)dt, x(0)=2x(0)=2, then, x(1)x(1) equals __________.MediumNumerical value
  5. 6 Apr 2024, Shift 1 · Q13Let y=y(x)y=y(x) be the solution of the differential equation (1+x2)dydx+y=etan⁡−1x(1+x^2)\frac{dy}{dx}+y=e^{\tan^{-1}x}, y(1)=0y(1)=0. Then y(0)y(0) isMediumSingle correct
  6. 5 Apr 2024, Shift 1 · Q12If y=y(x)y=y(x) is the solution of the differential equation dydx+2y=sin⁡(2x)\frac{dy}{dx}+2y=\sin(2x), y(0)=34y(0)=\frac34, then y(π8)y\left(\frac{\pi}{8}\right)…MediumSingle correct
  7. 5 Apr 2024, Shift 1 · Q26Let ff be a differentiable function in the interval (0,∞)(0,\infty) such that f(1)=1f(1)=1 and lim⁡t→xt2f(x)−x2f(t)t−x=1\lim_{t\to x}\frac{t^2f(x)-x^2f(t)}{t-x}=1 for…HardNumerical value
  8. 4 Apr 2024, Shift 2 · Q12Let y=y(x)y=y(x) be the solution of the differential equation (x2+4)2dy+(2x3y+8xy−2)dx=0(x^2+4)^2dy+(2x^3y+8xy-2)dx=0. If y(0)=0y(0)=0, then y(2)y(2) is equal toHardSingle correct
  9. 13 Apr 2023, Shift 2 · Q27If y=y(x)y=y(x) is the solution of the differential equation dydx+4x(x2−1)y=x+2(x2−1)52\frac{dy}{dx}+\frac{4x}{(x^2-1)}y=\frac{x+2}{(x^2-1)^{\frac{5}{2}}}, x>1x>1 such…HardNumerical value
  10. 12 Apr 2023, Shift 1 · Q11Let y=y(x)y=y(x), y>0y>0, be a solution curve of the differential equation (1+x2) dy=y(x−y) dx(1+x^2)\,dy=y(x-y)\,dx. If y(0)=1y(0)=1 and y(22)=βy(2\sqrt{2})=\beta, thenHardSingle correct
  11. 11 Apr 2023, Shift 2 · Q13Let y=y(x)y = y(x) be the solution of the differential equation dydx+5x(x5+1)y=(x5+1)2x7\frac{dy}{dx} + \frac{5}{x(x^5+1)}y = \frac{(x^5+1)^2}{x^7}, x>0x > 0. If…HardSingle correct
  12. 8 Apr 2023, Shift 1 · Q25If the solution curve of the differential equation (y−2log⁡ex)dx+(xlog⁡ex2)dy=0(y-2\log_e x)dx+(x\log_e x^2)dy=0, x>1x>1 passes through the points…MediumNumerical value
  13. 6 Apr 2023, Shift 2 · Q25Let a curve y=f(x), x∈(0,∞)y=f(x),\ x\in(0,\infty) pass through the points P(1,32)P\left(1,\frac{3}{2}\right) and Q(a,12)Q\left(a,\frac{1}{2}\right). If the…HardNumerical value
  14. 29 Jun 2022, Shift 2 · Q22Let y=y(x)y = y(x), x>1x > 1, be the solution of the differential equation (x−1)dydx+2xy=1x−1(x - 1)\frac{dy}{dx} + 2xy = \frac{1}{x - 1}, with…HardNumerical value
  15. 26 Jun 2022, Shift 2 · Q10If the solution of the differential equation dydx+ex(x2−2)y=(x2−2x)(x2−2)e2x\frac{dy}{dx} + e^x(x^2 - 2)y = (x^2 - 2x)(x^2 - 2)e^{2x} satisfies y(0)=0y(0) = 0, then the…HardSingle correct
  16. 29 Jul 2022, Shift 1 · Q7Let the solution curve y=y(x)y = y(x) of the differential equation (1+e2x)(dydx+y)=1(1 + e^{2x})\left(\frac{dy}{dx} + y\right) = 1 pass through the point…HardSingle correct
  17. 28 Jul 2022, Shift 2 · Q71Let y=y(x)y=y(x) be the solution curve of the differential equation dydx+1x2−1y=(x−1x+1)1/2, x>1\frac{dy}{dx}+\frac{1}{x^2-1}y=\left(\frac{x-1}{x+1}\right)^{1/2},\ x>1…HardSingle correct
  18. 17 Mar 2021, Shift 2 · Q68Let y=y(x)y=y(x) be the solution of the differential equation cos⁡x(3sin⁡x+cos⁡x+3)dy=(1+ysin⁡x(3sin⁡x+cos⁡x+3))dx\cos x(3\sin x+\cos x+3)dy=(1+y\sin x(3\sin x+\cos x+3))dx,…HardSingle correct
  19. 27 Aug 2021, Shift 1 · Q69Let y=y(x)y=y(x) be the solution of the differential equation dydx=2(y+2sin⁡x−5)x−2cos⁡x\frac{dy}{dx}=2(y+2\sin x-5)x-2\cos x such that y(0)=7y(0)=7. Then y(π)y(\pi) is…MediumSingle correct
  20. 26 Aug 2021, Shift 1 · Q76Let y=y(x)y=y(x) be a solution curve of the differential equation (y+1)tan⁡2x dx+tan⁡x dy+y dx=0(y+1)\tan^2 x\,dx+\tan x\,dy+y\,dx=0,…HardSingle correct
  21. 4 Sep 2020, Shift 1 · Q63Let y=y(x)y = y(x) be the solution of the differential equation, xy′−y=x2(xcos⁡x+sin⁡x)xy' - y = x^2(x\cos x + \sin x), x>0x > 0. If y(π)=πy(\pi) = \pi, then…HardSingle correct
  22. 9 Jan 2020, Shift 1 · Q74If for x≥0x\ge 0, y=y(x)y=y(x) is the solution of the differential equation, (x+1)dy=((x+1)2+y−3)dx(x+1)\mathrm{d}y=((x+1)^2+y-3)\mathrm{d}x, y(2)=0y(2)=0, then y(3)y(3)…MediumNumerical value

Shifts: 9 Jan 2020, Shift 1, 4 Sep 2020, Shift 1, 17 Mar 2021, Shift 2, 26 Aug 2021, Shift 1, 27 Aug 2021, Shift 1, 26 Jun 2022, Shift 2, 29 Jun 2022, Shift 2, 28 Jul 2022, Shift 2, 29 Jul 2022, Shift 1, 6 Apr 2023, Shift 2, 8 Apr 2023, Shift 1, 11 Apr 2023, Shift 2, 12 Apr 2023, Shift 1, 13 Apr 2023, Shift 2, 30 Jan 2024, Shift 1, 1 Feb 2024, Shift 1, 4 Apr 2024, Shift 2, 5 Apr 2024, Shift 1, 6 Apr 2024, Shift 1, 3 Apr 2025, Shift 1, 4 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