Let y = y(x) be the solution curve of the differential equation dy/dx = y/x (1 + xy^2(1 + log_e x) ), x > 0, y(1) = 3. Then (y^2(x))/9 is equal to :

(x^2)/(5 - 2x^3(2 + log_e x^3))

(x^2)/(7 - 3x^3(2 + log_e x^2))

(x^2)/(3x^3(1 + log_e x^2) - 2)

(x^2)/(2x^3(2 + log_e x^3) - 3)

Let y = y(x) be the solution curve of the differential… — JEE Main 2023 Mathematics PYQ

JEE Main 2023 · 25 Jan · Shift 1

Let

y = y(x)

be the solution curve of the differential equation

\frac{dy}{dx} = \frac{y}{x}\left(1 + xy^2(1 + \log_e x)\right)

x > 0

y(1) = 3

. Then

\frac{y^2(x)}{9}

is equal to :

Show answer

Correct option: B

[JEE Main 2023 · 25 Jan · Shift 1]

Practise Differential Equations the way it is asked

A timed set of real JEE Main Differential Equations questions, graded as the exam grades. No sign-up.