JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 25 July 2021, Shift 1, Maths Q85

Question 85 of 90 in this shift, Maths question 25 of 30, Section B.

Let

y=y(x)

be solution of the following differential equation

e^y\frac{dy}{dx}-2e^y\sin x+\sin x\cos^2x=0

y\left(\frac{\pi}{2}\right)=0

. If

y(0)=\log_e(\alpha+\beta e^{-2})

, then

4(\alpha+\beta)

is equal to _________.

Official answer

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Generalized Substitution for LDEs

Same idea in other shifts

Asked 6× in all

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
8 Apr 2024, Shift 2 · Q13Let $y = y(x)$ be the solution curve of the differential equation $\sec y \frac{dy}{dx} + 2x\sin y = x^3\cos y$ , $y(1) = 0$ . Then…MediumSingle correct
6 Apr 2023, Shift 2 · Q12If the solution curve $f(x,y)=0$ of the differential equation $\left(1+\log_e x\right)\frac{dx}{dy}-x\log_e x=e^y,\ x>0$ , passes through…HardSingle correct
26 Aug 2021, Shift 2 · Q68Let $y(x)$ be the solution of the differential equation $2x^2\,\mathrm{d}y+(\mathrm{e}^y-2x)\mathrm{d}x=0$ , $x>0$ . If $y(\mathrm{e})=1$ ,…HardSingle correct
26 Feb 2021, Shift 1 · Q84If $y=y(x)$ is the solution of the equation $e^{\sin y}\cos y\,\frac{dy}{dx}+e^{\sin y}\cos x=\cos x$ , $y(0)=0$ ; then…MediumNumerical value

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 108 of the 174 JEE Main shifts held from 2017 to 2026.