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 idea in other shifts

Asked 4× in all

4 Apr 2024, Shift 2 · Q27Let $y=y(x)$ be the solution of the differential equation $(x+y+2)^2dx=dy$ , $y(0)=-2$ . Let the maximum and minimum values of the function…HardNumerical value
1 Feb 2024, Shift 1 · Q11Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=2x(x+y)^3-x(x+y)-1$ , $y(0)=1$ . Then,…HardSingle correct
4 Sep 2020, Shift 2 · Q63The solution of the differential equation $\frac{dy}{dx} - \frac{y+3x}{\log_e (y+3x)} + 3 = 0$ is : (where C is a constant of integration.)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 108 of the 174 JEE Main shifts held from 2017 to 2026.