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Saturday, 31 October

JEE Main · Maths · Differential Equations

Initial Value Problem

JEE Main asked Initial Value Problem 15 times in 15 of the 108 shifts Lumi analysed, in 2017, 2020, 2021, 2022, 2023, 2024 and 2026. It belongs to Variable Separable Form, in Differential Equations (Maths). The longest wait between two years asking it was 3 years, across 2018 and 2019, which Lumi has no shifts for. In 2020, 2021, 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
15
in 15 shifts
Years
7 of 8
First asked
2017
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2017, 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.

00.510.86’170.33’200.07’210.07’220.07’230.19’240’250.11’26

Raw count: 2017: 1 in 1 shift · 2020: 4 in 12 shifts · 2021: 2 in 24 shifts · 2022: 2 in 24 shifts · 2023: 1 in 12 shifts · 2024: 4 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
  • 20244 of 18
  • 20231 of 12
  • 20222 of 24
  • 20212 of 24
  • 20204 of 12
  • 20171 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
  • Initial value problem for separable equation

Difficulty

Easy 2Medium 12Hard 1

3 of the 15 questions had a numerical answer.

Every question

All 15 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 1 · Q20Let y=y(x)y=y(x) be the solution of the differential equation dydx=(1+x+x2)(1−y+y2)\frac{dy}{dx}=(1+x+x^2)(1-y+y^2), y(0)=12y(0)=\frac12. Then (2y(1)−1)(2y(1)-1) is equal toMediumSingle correct
  2. 29 Jan 2024, Shift 1 · Q26If the solution curve y=y(x)y=y(x) of the differential equation (1+y2)(1+log⁡ex)dx+x dy=0(1+y^2)(1+\log_e x)dx+x\,dy=0, x>0x>0 passes through the point (1,1)(1,1) and…MediumNumerical value
  3. 27 Jan 2024, Shift 1 · Q13Let x=x(t)x=x(t) and y=y(t)y=y(t) be solutions of the differential equations dxdt+ax=0\dfrac{dx}{dt}+ax=0 and dydt+by=0\dfrac{dy}{dt}+by=0 respectively,…MediumSingle correct
  4. 9 Apr 2024, Shift 1 · Q11The solution curve, of the differential equation 2ydydx+3=5dydx2y\frac{dy}{dx}+3=5\frac{dy}{dx}, passing through the point (0,1)(0,1) is a conic, whose…MediumSingle correct
  5. 8 Apr 2024, Shift 1 · Q13Let y=y(x)y=y(x) be the solution of the differential equation (1+y2)etan⁡xdx+cos⁡2x (1+e2tan⁡x)dy=0(1+y^2)e^{\tan x}dx+\cos^2x\,(1+e^{2\tan x})dy=0, y(0)=1y(0)=1. Then…MediumSingle correct
  6. 13 Apr 2023, Shift 1 · Q14Let y=y1(x)y=y_1(x) and y=y2(x)y=y_2(x) be the solution curves of the differential equation dydx=y+7\frac{dy}{dx}=y+7 with initial conditions y1(0)=0y_1(0)=0…EasySingle correct
  7. 29 Jun 2022, Shift 2 · Q9If y=y (x)y = y\,(x) is the solution of the differential equation (1+e2x)dydx+2(1+y2)ex=0\left(1 + e^{2x}\right)\frac{dy}{dx} + 2\left(1 + y^2\right)e^x = 0 and…MediumSingle correct
  8. 26 Jun 2022, Shift 1 · Q30Let S=(0,2π)−{π2,3π4,3π2,7π4}S = (0, 2\pi) - \left\{\frac{\pi}{2}, \frac{3\pi}{4}, \frac{3\pi}{2}, \frac{7\pi}{4}\right\}. Let y=y(x)y = y(x), x∈Sx \in S, be the…HardNumerical value
  9. 17 Mar 2021, Shift 1 · Q72Which of the following is true for y(x)y(x) that satisfies the differential equation dydx=xy−1+x−y\frac{dy}{dx}=xy-1+x-y ; y(0)=0y(0)=0 :MediumSingle correct
  10. 25 Jul 2021, Shift 2 · Q86Let a curve y=f(x)y=f(x) pass through the point (2,(log⁡e2)2)(2,(\log_e 2)^2) and have slope 2yxlog⁡ex\frac{2y}{x\log_e x} for all positive real value of xx.…MediumNumerical value
  11. 5 Sep 2020, Shift 1 · Q63If y=y(x)y=y(x) is the solution of the differential equation 5+ex2+y⋅dydx+ex=0\frac{5+e^x}{2+y}\cdot\frac{dy}{dx}+e^x=0 satisfying y(0)=1y(0)=1, then a value of…EasySingle correct
  12. 3 Sep 2020, Shift 1 · Q62The solution curve of the differential equation, (1+e−x)(1+y2)dydx=y2(1+e^{-x})(1+y^2)\frac{dy}{dx}=y^2, which passes through the point (0, 1), is :MediumSingle correct
  13. 2 Sep 2020, Shift 1 · Q63Let y=y(x)y=y(x) be the solution of the differential equation, 2+sin⁡xy+1⋅dydx=−cos⁡x, y>0, y(0)=1\frac{2+\sin x}{y+1}\cdot\frac{dy}{dx}=-\cos x,\ y>0,\ y(0)=1. If y(π)=ay(\pi)=a…MediumSingle correct
  14. 8 Jan 2020, Shift 1 · Q62Let y=y(x)y=y(x) be a solution of the differential equation, 1−x2 dydx+1−y2=0\sqrt{1-x^2}\,\dfrac{dy}{dx}+\sqrt{1-y^2}=0, ∣x∣<1|x|<1. If…MediumSingle correct
  15. 2 Apr 2017 (offline) · Q77If (2+sin⁡x)dydx+(y+1)cos⁡x=0(2+\sin x)\frac{dy}{dx}+(y+1)\cos x=0 and y(0)=1y(0)=1, then y(π2)y\left(\frac{\pi}{2}\right) is equal to :MediumSingle correct

Shifts: 2 Apr 2017 (offline), 8 Jan 2020, Shift 1, 2 Sep 2020, Shift 1, 3 Sep 2020, Shift 1, 5 Sep 2020, Shift 1, 17 Mar 2021, Shift 1, 25 Jul 2021, Shift 2, 26 Jun 2022, Shift 1, 29 Jun 2022, Shift 2, 13 Apr 2023, Shift 1, 27 Jan 2024, Shift 1, 29 Jan 2024, Shift 1, 8 Apr 2024, Shift 1, 9 Apr 2024, Shift 1, 4 Apr 2026, Shift 1.

Same topic

Other ideas in Variable Separable Form

Variable Separable Form has 17 ideas JEE Main has asked; 8 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas