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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

4

NTA final key.

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

Same idea in other shifts

Asked 2× 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

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.