JEE Main Maths · Differential Equations

Linear Differential Equations in JEE Main

Name: Linear Differential Equations: JEE Main previous year questions
Creator: Lumi

Linear Differential Equations (Maths, Differential Equations) came 29 times in 28 of the 42 JEE Main shifts Lumi analysed, across 14 distinct ideas. 18 of them came in 2024–26; it was last asked in 2026.

Questions: 29; in 28 shifts
Ideas asked: 14; 8 asked more than once
Numerical answer: 12; 41% of its questions
Pattern: Asked most years; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 0Medium 12Hard 17

Format

Single correct17 Q
Numerical value12 Q

Ideas inside the topic

14 ideas

Integrating Factors with Trigonometric Functions6 Q
Integrating Factor Calculation3 Q
Particular Solution Solving3 Q
Linear in x Form3 Q
Generalized Substitution for LDEs2 Q
LDEs Disguised in Exact Differential Form2 Q
LDEs Formed via Leibniz Integral Rule2 Q
Standard Linear Form Identification2 Q
Asymptotic Behavior of LDE Solutions1 Q
Bernoulli Equation Reduction1 Q
Coefficient Normalization for Standard Form1 Q
General Solution Formula1 Q

Where it sits

Part of Differential Equations, which had 57 questions in all. Linear Differential Equations accounts for 51% of them. In Lumi's JEE taxonomy it belongs to Calculus.

Some questions sit in other chapters too: Application of Derivatives.

Every question

All 29 Linear Differential Equations questions

Newest first, each with its options and official answer.

2 Apr 2026, Shift 1 · Q20Let $y=y(x)$ be the solution curve of the differential equation $(1+\sin x)\frac{dy}{dx}+(y+1)\cos x=0$ , $y(0)=0$ . If the curve $y=y(x)$ …MediumSingle correct
4 Apr 2026, Shift 2 · Q19Let $y=y(x)$ be the solution of the differential equation:…HardSingle correct
5 Apr 2026, Shift 2 · Q25Let $y=y(x)$ be the solution of the differential equation $(\tan x)^{1/2}\,dy=\left(\sec^3 x-(\tan x)^{3/2}\,y\right)dx$ ,…HardNumerical value
6 Apr 2026, Shift 1 · Q25Let $y=y(x)$ be the solution of the differential equation…HardNumerical value
6 Apr 2026, Shift 2 · Q18Let $f:\mathbf{R}\to\mathbf{R}$ be such that $f(xy)=f(x)f(y)$ , for all $x,y\in\mathbf{R}$ and $f(0)\neq0$ . Let $g:[1,\infty)\to\mathbf{R}$ …HardSingle correct
8 Apr 2026, Shift 2 · Q17Let $y = y(x)$ be the solution of the differential equation $x\sqrt{1-x^2}\,dy + \left(y\sqrt{1-x^2} - x\cos^{-1}x\right)dx = 0$ ,…MediumSingle correct
2 Apr 2025, Shift 2 · Q25Let $y = y(x)$ be the solution of the differential equation…MediumNumerical value
3 Apr 2025, Shift 1 · Q20Let $g$ be a differentiable function such that $\int_0^x g(t)\,dt = x - \int_0^x t\,g(t)\,dt$ , $x \ge 0$ and let $y = y(x)$ satisfy the…HardSingle correct
3 Apr 2025, Shift 2 · Q20Let $y = y(x)$ be the solution of the differential equation…MediumSingle correct
4 Apr 2025, Shift 2 · Q20If a curve $y=y(x)$ passes through the point $\left(1,\frac{\pi}{2}\right)$ and satisfies the differential equation…HardSingle correct
7 Apr 2025, Shift 1 · Q20Let $y = y(x)$ be the solution curve of the differential equation $x(x^2 + e^x)\,dy + (e^x(x-2)y - x^3)\,dx = 0$ , $x > 0$ , passing through…HardSingle correct
7 Apr 2025, Shift 2 · Q19Let $y=y(x)$ be the solution of the differential equation $(x^2+1)y'-2xy=(x^4+2x^2+1)\cos x$ , $y(0)=1$ . Then $\int_{-3}^{3}y(x)\,dx$ is :MediumSingle correct
8 Apr 2025, Shift 2 · Q20Let $f(x) = x - 1$ and $g(x) = e^x$ for $x \in \mathbb{R}$ . If…HardSingle correct
9 Apr 2024, Shift 2 · Q26For a differentiable function $f:\mathbb{R}\to\mathbb{R}$ , suppose $f'(x)=3f(x)+\alpha$ , where $\alpha\in\mathbb{R}$ , $f(0)=1$ and…MediumNumerical value
29 Jan 2024, Shift 1 · Q13A function $y=f(x)$ satisfies $f(x)\sin 2x+\sin x-(1+\cos^2x)f'(x)=0$ with condition $f(0)=0$ . Then, $f\left(\frac{\pi}{2}\right)$ is…MediumSingle correct
30 Jan 2024, Shift 2 · Q27Let $Y = Y(X)$ be a curve lying in the first quadrant such that the area enclosed by the line $Y - y = Y'(x)(X - x)$ and the co-ordinate…HardNumerical value
31 Jan 2024, Shift 1 · Q11Let $y=y(x)$ be the solution of the differential equation…HardSingle correct
31 Jan 2024, Shift 2 · Q27Let $y=y(x)$ be the solution of the differential equation $\sec^2x\,dx+\left(e^{2y}\tan^2x+\tan x\right)dy=0$ , $0<x<\frac{\pi}{2}$ ,…HardNumerical value
6 Apr 2023, Shift 1 · Q29Let $y=y(x)$ be a solution of the differential equation $(x\cos x)\,dy+(xy\sin x+y\cos x-1)\,dx=0,\ 0<x<\frac{\pi}{2}$ . If…HardNumerical value
8 Apr 2023, Shift 2 · Q28Let the solution curve $x = x(y)$ , $0 < y < \frac{\pi}{2}$ , of the differential equation…HardNumerical value
13 Apr 2023, Shift 2 · Q27If $y=y(x)$ is the solution of the differential equation $\frac{dy}{dx}+\frac{4x}{(x^2-1)}y=\frac{x+2}{(x^2-1)^{\frac{5}{2}}}$ , $x>1$ such…HardNumerical value
28 Jul 2022, Shift 1 · Q10If $y=y(x),\ x\in(0,\pi/2)$ be the solution curve of the differential equation…HardSingle correct
28 Jul 2022, Shift 1 · Q20The minimum value of the twice differentiable function $f(x)=\int_0^x e^{x-t}f'(t)\,dt-(x^2-x+1)e^x,\ x\in\mathbf{R}$ , is :HardSingle correct
24 Jun 2022, Shift 1 · Q14If $x=x(y)$ is the solution of the differential equation $y\frac{dx}{dy}=2x+y^3(y+1)e^y,\ x(1)=0$ ; then $x(e)$ is equal to :MediumSingle correct
29 Jun 2022, Shift 1 · Q22Let $y = y(x)$ be the solution of the differential equation…HardNumerical value
3 Aug 2021, Shift 2 · Q87If the solution $y = y(x)$ of the differential equation $\left(y + 3x^4\right)\frac{dx}{dy} = x,\ x > 0$ , satisfies $y(1) = -1$ , then the…MediumNumerical value
25 Jul 2021, Shift 1 · Q85Let $y=y(x)$ be solution of the following differential equation $e^y\frac{dy}{dx}-2e^y\sin x+\sin x\cos^2x=0$ ,…MediumNumerical value
16 Mar 2021, Shift 2 · Q68If $y=y(x)$ is the solution of the differential equation $\frac{dy}{dx}+(\tan x)\,y=\sin x$ , $0\le x\le\frac{\pi}{3}$ , with $y(0)=0$ , then…MediumSingle correct
6 Sep 2020, Shift 2 · Q63If $y=\left(\frac{2}{\pi}x-1\right)\mathrm{cosec}\,x$ is the solution of the differential equation,…MediumSingle correct