JEE Main 2026 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 6 April 2026, Shift 1, 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

\left(x^2-x\sqrt{x^2-1}\right)dy+\left(y\left(x-\sqrt{x^2-1}\right)-x\right)dx=0

x\ge 1

. If

y(1)=1

, then the greatest integer less than

y\left(\sqrt{5}\right)

is ________.

Official answer

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Coefficient Normalization for Standard Form

Same idea in other shifts

Asked 3× in all

6 Apr 2024, Shift 1 · Q14Let $y=y(x)$ be the solution of the differential equation $(2x\log_e x)\frac{dy}{dx}+2y=\frac{3}{x}\log_e x$ , $x>0$ and $y(e^{-1})=0$ .…MediumSingle correct
28 Jun 2022, Shift 1 · Q11Let $y=y(x)$ be the solution of the differential equation $x(1-x^2)\frac{dy}{dx}+(3x^2y-y-4x^3)=0,\ x>1$ , with $y(2)=-2$ . Then $y(3)$ is…HardSingle correct

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.