Let $y=y(x)$ be the solution of the differential equation $(x+y+2)^2dx=dy$, $y(0)=-2$. Let the maximum and minimum values of the function $y=y(x)$ in $\left[0,\frac{\pi}{3}\right]$ be $\alpha$ and $\beta$, respectively. If $(3\alpha+\pi)^2+\beta^2=\gamma+\delta\sqrt3$, $\gamma,\delta\in\mathbb{Z}$, then $\gamma+\delta$ equals __________

JEE Main 2024 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 4 April 2024, Shift 2, Maths Q27

Question 27 of 90 in this shift, Maths question 27 of 30, Section B.

Let

y=y(x)

be the solution of the differential equation

(x+y+2)^2dx=dy

y(0)=-2

. Let the maximum and minimum values of the function

y=y(x)

\left[0,\frac{\pi}{3}\right]

\alpha

and

\beta

, respectively. If

(3\alpha+\pi)^2+\beta^2=\gamma+\delta\sqrt3

\gamma,\delta\in\mathbb{Z}

, then

\gamma+\delta

equals __________

Official answer

NTA final key.

Chapter: Differential Equations
Topic: Variable Separable Form
Idea tested: Reducible to Separable

Same idea in other shifts

Asked 4× in all

1 Feb 2024, Shift 1 · Q11Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=2x(x+y)^3-x(x+y)-1$ , $y(0)=1$ . Then,…HardSingle correct
25 Jul 2021, Shift 1 · Q62Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=1+xe^{y-x}$ , $-\sqrt2<x<\sqrt2$ , $y(0)=0$ then, the minimum value…HardSingle correct
4 Sep 2020, Shift 2 · Q63The solution of the differential equation $\frac{dy}{dx} - \frac{y+3x}{\log_e (y+3x)} + 3 = 0$ is : (where C is a constant of integration.)MediumSingle 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.