JEE Main 2025 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 2 April 2025, Shift 2, Maths Q25

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

Let

y = y(x)

be the solution of the differential equation

\frac{\mathrm{d}y}{\mathrm{d}x} + 2y\sec^2 x = 2\sec^2 x + 3\tan x\cdot\sec^2 x

such that

y(0) = \frac{5}{4}

. Then

12\left(y\left(\frac{\pi}{4}\right) - e^{-2}\right)

is equal to __________.

Official answer

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
3 Apr 2025, Shift 2 · Q20Let $y = y(x)$ be the solution of the differential equation…MediumSingle correct
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.