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Saturday, 10 October

JEE Main Maths · Class 12

Differential Equations: JEE Main previous year questions

Differential Equations had 57 questions in the 42 JEE Main shifts Lumi analysed, about 1.2 a shift, asked in 42 of 42 shifts. It ranks 8 of 22 Maths chapters by questions; 44% of its questions were hard.

Questions
57
in 42 of 42 shifts
A shift, on average
1.2
of 25 Maths questions
Since 2024
+0.2
1.1 a shift in 2017–23, 1.3 in 2024–26
Numerical answer
17
30% of its questions

Year by year

How often it came

Questions in the analysed shifts of each year. Years differ in how many shifts Lumi analysed, so read the bars with the shift count.

Questions each year
08161’174’206’217’224’2315’248’2512’26

2017: 1 shifts · 2020: 4 shifts · 2021: 4 shifts · 2022: 4 shifts · 2023: 4 shifts · 2024: 8 shifts · 2025: 8 shifts · 2026: 9 shifts

Difficulty by year
  • 20171
  • 20204
  • 20216
  • 20227
  • 20234
  • 202415
  • 20258
  • 202612
  • Easy
  • Medium
  • Hard

Inside the chapter

Topics and the ideas that repeat

7 topics and 28 distinct ideas; 11 ideas were asked more than once. Most questions are single correct and multi-step.

Topics, by questions

2 questions had no close topic in our taxonomy and are counted for the chapter only.

Ideas asked most
11 repeat

Study it on Lumi

Differential Equations: the interactive lesson

Every question

All 57 Differential Equations questions

Newest first. Each opens with its options and the official answer.

2026 12 questions

  1. 2 Apr 2026, Shift 1 · Q17If the curve y=f(x)y=f(x) passes through the point (1,e)(1, e) and satisfies the differential equation dy=y(2+log⁡ex) dxdy=y(2+\log_e x)\,dx, x>0x>0, then f(e)f(e)…EasySingle correct
  2. 2 Apr 2026, Shift 1 · Q20Let y=y(x)y=y(x) be the solution curve of the differential equation (1+sin⁡x)dydx+(y+1)cos⁡x=0(1+\sin x)\frac{dy}{dx}+(y+1)\cos x=0, y(0)=0y(0)=0. If the curve y=y(x)y=y(x)…MediumSingle correct
  3. 2 Apr 2026, Shift 2 · Q20Let x=x(y)x = x(y) be the solution of the differential equation 2y2dxdy−2xy+x2=0,y>1,x(e)=e2y^2\frac{dx}{dy} - 2xy + x^2 = 0, y > 1, x(e) = e. Then x(e2)x(e^2) is equal to:MediumSingle correct
  4. 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
  5. 4 Apr 2026, Shift 2 · Q19Let y=y(x)y=y(x) be the solution of the differential equation:…HardSingle correct
  6. 4 Apr 2026, Shift 2 · Q25Let ff be a twice differentiable function such that f(x)=∫0xtan⁡(t−x) dt−∫0xf(t)tan⁡t dtf(x)=\int_0^x\tan(t-x)\,dt-\int_0^x f(t)\tan t\,dt,…HardNumerical value
  7. 5 Apr 2026, Shift 1 · Q25Let y=y(x)y = y(x) be the solution of the differential equation…HardNumerical value
  8. 5 Apr 2026, Shift 2 · Q19Let f:[1,∞)→Rf:[1,\infty)\to\mathbf{R} be a differentiable function defined as f(x)=∫1xf(t) dt+(1−x)(log⁡ex−1)+ef(x)=\int_1^x f(t)\,dt+(1-x)(\log_e x-1)+e. Then the value of…HardSingle correct
  9. 5 Apr 2026, Shift 2 · Q25Let y=y(x)y=y(x) be the solution of the differential equation (tan⁡x)1/2 dy=(sec⁡3x−(tan⁡x)3/2 y)dx(\tan x)^{1/2}\,dy=\left(\sec^3 x-(\tan x)^{3/2}\,y\right)dx,…HardNumerical value
  10. 6 Apr 2026, Shift 1 · Q25Let y=y(x)y=y(x) be the solution of the differential equation…HardNumerical value
  11. 6 Apr 2026, Shift 2 · Q18Let f:R→Rf:\mathbf{R}\to\mathbf{R} be such that f(xy)=f(x)f(y)f(xy)=f(x)f(y), for all x,y∈Rx,y\in\mathbf{R} and f(0)≠0f(0)\neq0. Let g:[1,∞)→Rg:[1,\infty)\to\mathbf{R}…HardSingle correct
  12. 8 Apr 2026, Shift 2 · Q17Let y=y(x)y = y(x) be the solution of the differential equation x1−x2 dy+(y1−x2−xcos⁡−1x)dx=0x\sqrt{1-x^2}\,dy + \left(y\sqrt{1-x^2} - x\cos^{-1}x\right)dx = 0,…MediumSingle correct

2025 8 questions

  1. 2 Apr 2025, Shift 1 · Q24Let f:R→Rf:\mathbf{R}\to\mathbf{R} be a thrice differentiable odd function satisfying f′(x)≥0f'(x)\ge0, f′′(x)=f(x)f''(x)=f(x), f(0)=0f(0)=0, f′(0)=3f'(0)=3. Then…MediumNumerical value
  2. 2 Apr 2025, Shift 2 · Q25Let y=y(x)y = y(x) be the solution of the differential equation…MediumNumerical value
  3. 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
  4. 3 Apr 2025, Shift 2 · Q20Let y=y(x)y = y(x) be the solution of the differential equation…MediumSingle correct
  5. 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
  6. 7 Apr 2025, Shift 1 · Q20Let y=y(x)y = y(x) be the solution curve of the differential equation x(x2+ex) dy+(ex(x−2)y−x3) dx=0x(x^2 + e^x)\,dy + (e^x(x-2)y - x^3)\,dx = 0, x>0x > 0, passing through…HardSingle correct
  7. 7 Apr 2025, Shift 2 · Q19Let y=y(x)y=y(x) be the solution of the differential equation (x2+1)y′−2xy=(x4+2x2+1)cos⁡x(x^2+1)y'-2xy=(x^4+2x^2+1)\cos x, y(0)=1y(0)=1. Then ∫−33y(x) dx\int_{-3}^{3}y(x)\,dx is :MediumSingle correct
  8. 8 Apr 2025, Shift 2 · Q20Let f(x)=x−1f(x) = x - 1 and g(x)=exg(x) = e^x for x∈Rx \in \mathbb{R}. If…HardSingle correct

2024 15 questions

  1. 6 Apr 2024, Shift 2 · Q13Suppose the solution of the differential equation dydx=(2+α)x−βy+2βx−2αy−(βγ−4α)\frac{dy}{dx}=\frac{(2+\alpha)x-\beta y+2}{\beta x-2\alpha y-(\beta\gamma-4\alpha)}…HardSingle correct
  2. 6 Apr 2024, Shift 2 · Q26If the solution y(x)y(x) of the given differential equation (ey+1)cos⁡x dx+eysin⁡x dy=0(e^y+1)\cos x\,dx+e^y\sin x\,dy=0 passes through the point…EasyNumerical value
  3. 8 Apr 2024, Shift 1 · Q12Let f(x)f(x) be a positive function such that the area bounded by y=f(x)y=f(x), y=0y=0 from x=0x=0 to x=a>0x=a>0 is e−a+4a2+a−1e^{-a}+4a^2+a-1. Then the…HardSingle correct
  4. 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
  5. 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
  6. 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
  7. 9 Apr 2024, Shift 2 · Q13Let ∫0x1−(y′(t))2 dt=∫0xy(t) dt, 0≤x≤3, y≥0, y(0)=0\int_0^x\sqrt{1-(y'(t))^2}\,dt=\int_0^x y(t)\,dt,\ 0\le x\le 3,\ y\ge0,\ y(0)=0. Then at x=2x=2, y′′+y+1y''+y+1 is equal toHardSingle correct
  8. 9 Apr 2024, Shift 2 · Q26For a differentiable function f:R→Rf:\mathbb{R}\to\mathbb{R}, suppose f′(x)=3f(x)+αf'(x)=3f(x)+\alpha, where α∈R\alpha\in\mathbb{R}, f(0)=1f(0)=1 and…MediumNumerical value
  9. 29 Jan 2024, Shift 1 · Q13A function y=f(x)y=f(x) satisfies f(x)sin⁡2x+sin⁡x−(1+cos⁡2x)f′(x)=0f(x)\sin 2x+\sin x-(1+\cos^2x)f'(x)=0 with condition f(0)=0f(0)=0. Then, f(π2)f\left(\frac{\pi}{2}\right) is…MediumSingle correct
  10. 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
  11. 30 Jan 2024, Shift 2 · Q27Let Y=Y(X)Y = Y(X) be a curve lying in the first quadrant such that the area enclosed by the line Y−y=Y′(x)(X−x)Y - y = Y'(x)(X - x) and the co-ordinate…HardNumerical value
  12. 31 Jan 2024, Shift 1 · Q11Let y=y(x)y=y(x) be the solution of the differential equation…HardSingle correct
  13. 31 Jan 2024, Shift 1 · Q12The solution curve of the differential equation ydxdy=x(log⁡ex−log⁡ey+1), x>0, y>0y\frac{dx}{dy}=x(\log_ex-\log_ey+1),\ x>0,\ y>0 passing through the point (e,1)(e,1) isMediumSingle correct
  14. 31 Jan 2024, Shift 2 · Q13The temperature T(t)T(t) of a body at time t=0t=0 is 160∘160^\circ F and it decreases continuously as per the differential equation…EasySingle correct
  15. 31 Jan 2024, Shift 2 · Q27Let y=y(x)y=y(x) be the solution of the differential equation sec⁡2x dx+(e2ytan⁡2x+tan⁡x)dy=0\sec^2x\,dx+\left(e^{2y}\tan^2x+\tan x\right)dy=0, 0<x<π20<x<\frac{\pi}{2},…HardNumerical value

2023 4 questions

  1. 6 Apr 2023, Shift 1 · Q29Let y=y(x)y=y(x) be a solution of the differential equation (xcos⁡x) dy+(xysin⁡x+ycos⁡x−1) dx=0, 0<x<π2(x\cos x)\,dy+(xy\sin x+y\cos x-1)\,dx=0,\ 0<x<\frac{\pi}{2}. If…HardNumerical value
  2. 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
  3. 11 Apr 2023, Shift 1 · Q20Let y=y(x)y = y(x) be a solution curve of the differential equation. (1−x2y2) dx=y dx+x dy(1 - x^2y^2)\,dx = y\,dx + x\,dy. If the line x=1x = 1 intersects the…MediumSingle correct
  4. 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

2022 7 questions

  1. 25 Jul 2022, Shift 1 · Q10The slope of the tangent to a curve C:y=y(x)C:y=y(x) at any point (x,y)(x,y) on it is…HardSingle correct
  2. 25 Jul 2022, Shift 1 · Q11The general solution of the differential equation (x−y2) dx+y(5x+y2) dy=0(x-y^2)\,dx+y(5x+y^2)\,dy=0 is :HardSingle correct
  3. 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
  4. 28 Jul 2022, Shift 1 · Q10If y=y(x), x∈(0,π/2)y=y(x),\ x\in(0,\pi/2) be the solution curve of the differential equation…HardSingle correct
  5. 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
  6. 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
  7. 29 Jun 2022, Shift 1 · Q22Let y=y(x)y = y(x) be the solution of the differential equation…HardNumerical value

2021 6 questions

  1. 3 Aug 2021, Shift 2 · Q73A curve passes through the point (−1,4)(-1, 4). If the normal to it at any point (x,y)(x, y) on it passes through (2,0)(2, 0), then its equation isMediumSingle correct
  2. 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
  3. 25 Jul 2021, Shift 1 · Q62Let y=y(x)y=y(x) be the solution of the differential equation dydx=1+xey−x\frac{dy}{dx}=1+xe^{y-x}, −2<x<2-\sqrt2<x<\sqrt2, y(0)=0y(0)=0 then, the minimum value…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. 16 Mar 2021, Shift 2 · Q68If y=y(x)y=y(x) is the solution of the differential equation dydx+(tan⁡x) y=sin⁡x\frac{dy}{dx}+(\tan x)\,y=\sin x, 0≤x≤π30\le x\le\frac{\pi}{3}, with y(0)=0y(0)=0, then…MediumSingle correct
  6. 18 Mar 2021, Shift 1 · Q74The differential equation satisfied by the system of parabolas y2=4a(x+a)y^2=4a(x+a) is :MediumSingle correct

2020 4 questions

  1. 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
  2. 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
  3. 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
  4. 6 Sep 2020, Shift 2 · Q63If y=(2πx−1)cosec xy=\left(\frac{2}{\pi}x-1\right)\mathrm{cosec}\,x is the solution of the differential equation,…MediumSingle correct

2017 1 questions

  1. 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

Pattern: Asked most years.