JEE Main Maths · Differential Equations

Variable Separable Form in JEE Main

Name: Variable Separable Form: JEE Main previous year questions
Creator: Lumi

Variable Separable Form (Maths, Differential Equations) came 12 times in 12 of the 42 JEE Main shifts Lumi analysed, across 6 distinct ideas. 7 of them came in 2024–26; it was last asked in 2026.

Questions: 12; in 12 shifts
Ideas asked: 6; 1 asked more than once
Numerical answer: 2; 17% 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 3Medium 8Hard 1

Format

Single correct10 Q
Numerical value2 Q

Ideas inside the topic

6 ideas

Initial Value Problem7 Q
Separability Check1 Q
Direct Integration1 Q
Physical Modeling Applications1 Q
Substitution of Product (u = xy)1 Q
Reducible to Separable1 Q

Where it sits

Part of Differential Equations, which had 57 questions in all. Variable Separable Form accounts for 21% of them. In Lumi's JEE taxonomy it belongs to Calculus.

Every question

All 12 Variable Separable Form questions

Newest first, each with its options and official answer.

2 Apr 2026, Shift 1 · Q17If the curve $y=f(x)$ passes through the point $(1, e)$ and satisfies the differential equation $dy=y(2+\log_e x)\,dx$ , $x>0$ , then $f(e)$ …EasySingle correct
4 Apr 2026, Shift 1 · Q20Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=(1+x+x^2)(1-y+y^2)$ , $y(0)=\frac12$ . Then $(2y(1)-1)$ is equal toMediumSingle correct
6 Apr 2024, Shift 2 · Q26If the solution $y(x)$ of the given differential equation $(e^y+1)\cos x\,dx+e^y\sin x\,dy=0$ passes through the point…EasyNumerical value
8 Apr 2024, Shift 1 · Q13Let $y=y(x)$ be the solution of the differential equation $(1+y^2)e^{\tan x}dx+\cos^2x\,(1+e^{2\tan x})dy=0$ , $y(0)=1$ . Then…MediumSingle correct
9 Apr 2024, Shift 1 · Q11The solution curve, of the differential equation $2y\frac{dy}{dx}+3=5\frac{dy}{dx}$ , passing through the point $(0,1)$ is a conic, whose…MediumSingle correct
29 Jan 2024, Shift 1 · Q26If the solution curve $y=y(x)$ of the differential equation $(1+y^2)(1+\log_e x)dx+x\,dy=0$ , $x>0$ passes through the point $(1,1)$ and…MediumNumerical value
31 Jan 2024, Shift 2 · Q13The temperature $T(t)$ of a body at time $t=0$ is $160^\circ$ F and it decreases continuously as per the differential equation…EasySingle correct
11 Apr 2023, Shift 1 · Q20Let $y = y(x)$ be a solution curve of the differential equation. $(1 - x^2y^2)\,dx = y\,dx + x\,dy$ . If the line $x = 1$ intersects the…MediumSingle correct
25 Jul 2021, Shift 1 · Q62Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=1+xe^{y-x}$ , $-\sqrt2<x<\sqrt2$ , $y(0)=0$ then, the minimum value…HardSingle correct
8 Jan 2020, Shift 1 · Q62Let $y=y(x)$ be a solution of the differential equation, $\sqrt{1-x^2}\,\dfrac{dy}{dx}+\sqrt{1-y^2}=0$ , $|x|<1$ . If…MediumSingle correct
2 Sep 2020, Shift 1 · Q63Let $y=y(x)$ be the solution of the differential equation, $\frac{2+\sin x}{y+1}\cdot\frac{dy}{dx}=-\cos x,\ y>0,\ y(0)=1$ . If $y(\pi)=a$ …MediumSingle correct
2 Apr 2017 (offline) · Q77If $(2+\sin x)\frac{dy}{dx}+(y+1)\cos x=0$ and $y(0)=1$ , then $y\left(\frac{\pi}{2}\right)$ is equal to :MediumSingle correct