JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 26 June 2022, Shift 2, Maths Q10

Question 10 of 90 in this shift, Maths question 10 of 30, Section A.

If the solution of the differential equation

\frac{dy}{dx} + e^x(x^2 - 2)y = (x^2 - 2x)(x^2 - 2)e^{2x}

satisfies

y(0) = 0

, then the value of

y(2)

is ______

(1) $-1$
(2) $1$
(3) $0$ Official answer
(4) $e$

Official answer

Option 3

NTA final key.

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.