The solution curve, of the differential equation 2 y d y/d x+3=5 d y/d x , passing through the point (0,1) is a conic, whose vertex lies on the line :

Mathematics · Differential Equations

JEE Main 2024 — 9 April, Shift 1 — Question 3

The solution curve, of the differential equation $2 y \frac{d y}{d x}+3=5 \frac{d y}{d x}$ , passing through the point $(0,1)$ is a conic, whose vertex lies on the line :

Option A:
$2 x+3 y=9$
Correct
Option B:
$2 x+3 y=-9$
Option C:
$2 x+3 y=-6$
Option D:
$2 x+3 y=6$

Answer: A

Step-by-step solution

$(2 y-5) \frac{d y}{d x}=-3$ $(2 y-5) d y=-3 d x$

$2 \cdot \frac{y^{2}}{2}-5 y=-3 x+\lambda$

$\because$ Curve passes through $(0,1)$

$\Rightarrow \lambda=-4$

$\because$ Curve will be $\left(y-\frac{5}{2}\right)^{2}=-3\left(x-\frac{3}{4}\right)$

$\therefore$ Vertex of parabola will be $\left(\frac{3}{4}, \frac{5}{2}\right)$

$\because 2 x+3 y=9$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 9 April, Shift 1
Subject: Mathematics
Chapter: Differential Equations
Topic: Methods of solving a First Order,First Degree Differential

The solution of the differential equation (x^2 + y^2) dx - 5xy dy = 0 , with y(1) = 0 , is:

Answer: A

Step-by-step solution

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