JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 3 April 2025, Shift 2, Maths Q20

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

Let

y = y(x)

be the solution of the differential equation

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

. Then

y\left(\frac{\pi}{4}\right)

is equal to

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

Official answer

Option 4

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Integrating Factors with Trigonometric Functions

Same idea in other shifts

Asked 7× in all

2 Apr 2026, Shift 1 · Q20Let $y=y(x)$ be the solution curve of the differential equation $(1+\sin x)\frac{dy}{dx}+(y+1)\cos x=0$ , $y(0)=0$ . If the curve $y=y(x)$ …MediumSingle correct
2 Apr 2025, Shift 2 · Q25Let $y = y(x)$ be the solution of the differential equation…MediumNumerical value
29 Jan 2024, Shift 1 · Q13A function $y=f(x)$ satisfies $f(x)\sin 2x+\sin x-(1+\cos^2x)f'(x)=0$ with condition $f(0)=0$ . Then, $f\left(\frac{\pi}{2}\right)$ is…MediumSingle correct
31 Jan 2024, Shift 1 · Q11Let $y=y(x)$ be the solution of the differential equation…HardSingle correct
28 Jul 2022, Shift 1 · Q10If $y=y(x),\ x\in(0,\pi/2)$ be the solution curve of the differential equation…HardSingle correct
27 Jun 2022, Shift 2 · Q28Let $y=y(x)$ be the solution of the differential equation $\left(1-x^2\right)dy=\left(xy+\left(x^3+2\right)\sqrt{1-x^2}\right)dx$ ,…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 108 of the 174 JEE Main shifts held from 2017 to 2026.