JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 7 April 2025, Shift 2, Maths Q19

Question 19 of 75 in this shift, Maths question 19 of 25, Section A.

Let

y=y(x)

be the solution of the differential equation

(x^2+1)y'-2xy=(x^4+2x^2+1)\cos x

y(0)=1

. Then

\int_{-3}^{3}y(x)\,dx

is :

(1)18
(2)24Official answer
(3)30
(4)36

Official answer

Option 2

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: General Solution Formula

Same idea in other shifts

Asked 3× in all

5 Apr 2024, Shift 2 · Q26Let $y = y(x)$ be the solution of the differential equation $\frac{dy}{dx} + \frac{2x}{(1+x^2)^2}\,y = x e^{\frac{1}{(1+x^2)}}$ ;…MediumNumerical value
25 Feb 2021, Shift 1 · Q69If a curve passes through the origin and the slope of the tangent to it at any point $(x, y)$ is $\frac{x^2 - 4x + y + 8}{x - 2}$ , then…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.