JEE Main 2020 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 4 September 2020, Shift 1, Maths Q63

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

Let

y = y(x)

be the solution of the differential equation,

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

x > 0

. If

y(\pi) = \pi

, then

y''\left(\frac{\pi}{2}\right) + y\left(\frac{\pi}{2}\right)

is equal to :

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

Official answer

Option 3

NTA final key (Sep 2020).

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Integrating Factor Calculation

Same idea in other shifts

Asked 22× in all

4 Apr 2026, Shift 2 · Q19Let $y=y(x)$ be the solution of the differential equation:…HardSingle correct
3 Apr 2025, Shift 1 · Q20Let $g$ be a differentiable function such that $\int_0^x g(t)\,dt = x - \int_0^x t\,g(t)\,dt$ , $x \ge 0$ and let $y = y(x)$ satisfy the…HardSingle correct
4 Apr 2024, Shift 2 · Q12Let $y=y(x)$ be the solution of the differential equation $(x^2+4)^2dy+(2x^3y+8xy-2)dx=0$ . If $y(0)=0$ , then $y(2)$ is equal toHardSingle correct
5 Apr 2024, Shift 1 · Q12If $y=y(x)$ is the solution of the differential equation $\frac{dy}{dx}+2y=\sin(2x)$ , $y(0)=\frac34$ , then $y\left(\frac{\pi}{8}\right)$ …MediumSingle correct
5 Apr 2024, Shift 1 · Q26Let $f$ be a differentiable function in the interval $(0,\infty)$ such that $f(1)=1$ and $\lim_{t\to x}\frac{t^2f(x)-x^2f(t)}{t-x}=1$ for…HardNumerical value
6 Apr 2024, Shift 1 · Q13Let $y=y(x)$ be the solution of the differential equation $(1+x^2)\frac{dy}{dx}+y=e^{\tan^{-1}x}$ , $y(1)=0$ . Then $y(0)$ isMediumSingle correct
1 Feb 2024, Shift 1 · Q28If $x=x(t)$ is the solution of the differential equation $(t+1)dx=(2x+(t+1)^4)dt$ , $x(0)=2$ , then, $x(1)$ equals __________.MediumNumerical value
30 Jan 2024, Shift 1 · Q26Let $y=y(x)$ be the solution of the differential equation $(1-x^2)dy=\left[xy+(x^3+2)\sqrt{3(1-x^2)}\right]dx$ , $-1<x<1$ , $y(0)=0$ . If…MediumNumerical 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.