JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 25 July 2021, Shift 1, Maths Q62

Question 62 of 90 in this shift, Maths question 2 of 30, Section A.

Let

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 of

y(x)

x\in(-\sqrt2,\sqrt2)

is equal to :

(1) $(1-\sqrt3)-\log_e(\sqrt3-1)$ Official answer
(2) $(1+\sqrt3)-\log_e(\sqrt3-1)$
(3) $(2-\sqrt3)-\log_e2$
(4) $(2+\sqrt3)+\log_e2$

Official answer

Option 1

NTA final key.

Chapter: Differential Equations
Topic: Variable Separable Form
Idea tested: Reducible to Separable

Same topic in other shifts

All Variable Separable Form questions

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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.