JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 September 2020, Shift 2, Maths Q63

Question 63 of 75 in this shift, Maths question 13 of 25.

The 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.)

(1) $x - \log_e(y+3x) = C$
(2) $x - 2\log_e(y+3x) = C$
(3) $x - \frac{1}{2}(\log_e(y+3x))^2 = C$ Official answer
(4) $y + 3x - \frac{1}{2}(\log_e x)^2 = C$

Official answer

Option 3

NTA final key (Sep 2020).

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
25 Jul 2021, Shift 1 · Q62Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=1+xe^{y-x}$ , $-\sqrt2<x<\sqrt2$ , $y(0)=0$ then, the minimum value…HardSingle 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.