JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 31 January 2024, Shift 1, Maths Q12

Question 12 of 90 in this shift, Maths question 12 of 30, Section A.

The 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)

(1) $2\left|\log_e\frac{x}{y}\right|=y+1$
(2) $\left|\log_e\frac{y}{x}\right|=y^2$
(3) $\left|\log_e\frac{y}{x}\right|=x$
(4) $\left|\log_e\frac{x}{y}\right|=y$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Differential Equations
Topic: Homogeneous Equations
Idea tested: Alternative Substitution x = vy

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
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
25 Jul 2022, Shift 1 · Q11The general solution of the differential equation $(x-y^2)\,dx+y(5x+y^2)\,dy=0$ is :HardSingle correct
28 Jul 2022, Shift 1 · Q1Let the solution curve of the differential equation $x\,dy=\left(\sqrt{x^2+y^2}+y\right)dx,\ x>0$ , intersect the line $x=1$ at $y=0$ and…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 42 of the 174 JEE Main shifts held from 2017 to 2026.