JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 24 June 2022, Shift 1, Maths Q14

Question 14 of 90 in this shift, Maths question 14 of 30, Section A.

x=x(y)

is the solution of the differential equation

y\frac{dx}{dy}=2x+y^3(y+1)e^y,\ x(1)=0

; then

x(e)

is equal to :

(1) $e^3(e^e-1)$ Official answer
(2) $e^e(e^3-1)$
(3) $e^2(e^e+1)$
(4) $e^e(e^2-1)$

Official answer

Option 1

NTA final key (2022 Session 1).

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Linear in x Form

Same idea in other shifts

Asked 3× in all

8 Apr 2023, Shift 2 · Q28Let the solution curve $x = x(y)$ , $0 < y < \frac{\pi}{2}$ , of the differential equation…HardNumerical value
3 Aug 2021, Shift 2 · Q87If the solution $y = y(x)$ of the differential equation $\left(y + 3x^4\right)\frac{dx}{dy} = x,\ x > 0$ , satisfies $y(1) = -1$ , then the…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 42 of the 174 JEE Main shifts held from 2017 to 2026.