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JEE Main 20249 AprilMorning Shift

Exam: JEE Main
Year: 2024
Date: 9 April
Shift: Morning Shift
Subject: Mathematics
Chapter: Differential Equations

JEE Main 2024 · 9 April · Morning Shift · Mathematics · Differential Equations

The solution curve, of the differential equation 2 y d y ~d x +3=5...

The solution curve, of the differential equation

2 y \frac{\mathrm{d} y}{\mathrm{~d} x}+3=5 \frac{\mathrm{d} y}{\mathrm{~d} x}

, passing through the point

(0,1)

is a conic, whose vertex lies on the line:

Options

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

Correct answer

A. $2 x+3 y=9$

Step-by-step solution

\begin{aligned} & (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\end{aligned}

\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

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