JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 22 July 2021, Shift 2, Maths Q90

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

Let

y=y(x)

be the solution of the differential equation

\left((x+2)\,e^{\left(\frac{y+1}{x+2}\right)}+(y+1)\right)dx=(x+2)\,dy

y(1)=1

. If the domain of

y=y(x)

is an open interval

(\alpha, \beta)

, then

|\alpha+\beta|

is equal to ________.

Official answer

1 or 4

NTA final key.

Chapter: Differential Equations
Topic: Homogeneous Equations
Idea tested: Domain Restrictions from Initial Value Problems

Same topic in other shifts

All Homogeneous Equations questions

2 Apr 2026, Shift 2 · Q20Let $x = x(y)$ be the solution of the differential equation $2y^2\frac{dx}{dy} - 2xy + x^2 = 0, y > 1, x(e) = e$ . Then $x(e^2)$ is equal to:MediumSingle correct
5 Apr 2026, Shift 1 · Q25Let $y = y(x)$ be the solution of the differential equation…HardNumerical value
6 Apr 2024, Shift 2 · Q13Suppose the solution of the differential equation $\frac{dy}{dx}=\frac{(2+\alpha)x-\beta y+2}{\beta x-2\alpha y-(\beta\gamma-4\alpha)}$ …HardSingle correct
8 Apr 2024, Shift 2 · Q27Let $\alpha|x| = |y|e^{xy-\beta}$ , $\alpha, \beta \in \mathbb{N}$ be the solution of the differential equation…HardNumerical value
9 Apr 2024, Shift 1 · Q10The solution of the differential equation $(x^2+y^2)dx-5xy\,dy=0$ , $y(1)=0$ , is :MediumSingle correct
31 Jan 2024, Shift 1 · Q12The solution curve of the differential equation $y\frac{dx}{dy}=x(\log_ex-\log_ey+1),\ x>0,\ y>0$ passing through the point $(e,1)$ isMediumSingle 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.