JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 April 2024, Shift 1, Maths Q13

Question 13 of 90 in this shift, Maths question 13 of 30, Section A.

Let

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

y\left(\frac{\pi}{4}\right)

is equal to

(1) $\frac{1}{e^2}$
(2) $\frac{1}{e}$ Official answer
(3) $\frac{2}{e}$
(4) $\frac{2}{e^2}$

Official answer

Option 2

NTA final key.

Chapter: Differential Equations
Topic: Variable Separable Form
Idea tested: Initial Value Problem

Same idea in other shifts

Asked 7× in all

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
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

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.