JEE Main 2026 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 4 April 2026, 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:

\frac{dy}{dx}+\left(\frac{6x^2+\left(3x^2+2x^3+4\right)e^{-2x}}{\left(x^3+2\right)\left(2+e^{-2x}\right)}\right)y=2+e^{-2x}

x\in(-1,2)

, satisfying

y(0)=\frac32

. If

y(1)=\alpha(2+e^{-2})

, then

\alpha

is equal to:

(1) $\frac{13}{8}$
(2) $\frac{6}{13}$
(3) $\frac{12}{13}$
(4) $\frac{13}{12}$ Official answer

Official answer

Option 4

NTA final key.

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

Same idea in other shifts

Asked 22× in all

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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
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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
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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
6 Apr 2023, Shift 2 · Q25Let a curve $y=f(x),\ x\in(0,\infty)$ pass through the points $P\left(1,\frac{3}{2}\right)$ and $Q\left(a,\frac{1}{2}\right)$ . If the…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.