JEE Main Maths · Differential Equations

Initial Value Problem

Initial Value Problem (Differential Equations) was asked 7 times in 7 JEE Main shifts, 2017–2026, out of the 42 shifts Lumi analysed. 1 of the 7 had a numerical answer.

Times asked: 7; in 7 shifts
Years: 2017–2026
Usual format: Single correct; Multi-step
Pattern: Frequent; repeats across shifts

How it is asked

Solve initial value differential equation
Initial value problem for separable equation

Difficulty

Easy 0Medium 7Hard 0

Where it sits

Chapter: Differential Equations. Topic: Variable Separable Form, 12 questions over 6 ideas.

Every time it came

All 7 questions

Newest first, each with its options and official answer.

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
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
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