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JEE Main 2025 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 7 April 2025, Shift 1, Maths Q20

Question 20 of 75 in this shift, Maths question 20 of 25, Section A.

Let

y = y(x)

be the solution curve of the differential equation

x(x^2 + e^x)\,dy + (e^x(x-2)y - x^3)\,dx = 0

,

x > 0

, passing through the point

(1, 0)

. Then

y(2)

is equal to

(1) $\frac{4}{4-e^2}$
(2) $\frac{2}{2-e^2}$
(3) $\frac{4}{4+e^2}$ Official answer
(4) $\frac{2}{2+e^2}$

Official answer

Option 3

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: LDEs Disguised in Exact Differential Form

Same idea in other shifts

Asked 2× in all

6 Apr 2023, Shift 1 · Q29Let $y=y(x)$ be a solution of the differential equation $(x\cos x)\,dy+(xy\sin x+y\cos x-1)\,dx=0,\ 0<x<\frac{\pi}{2}$ . If…HardNumerical 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.