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Consider the curve which is represented by the differential equation dy dx = 1 + x + y + xy. If it passes through the point (0,0), then which of the…

CUET UG 2025 — Mathematics Calculus

2025mcqmedium

Consider the curve which is represented by the differential equation dydx=1+x+y+xy\frac{dy}{dx} = 1 + x + y + xydxdy​=1+x+y+xy. If it passes through the point (0,0)(0,0)(0,0), then which of the following is/are true?

(A) it is a straight line.

(B) it is a parabola.

(C) it also passes through the point (−1,1e−1)(-1, \frac{1}{\sqrt{e}} - 1)(−1,e​1​−1)

(D) Its equation is xy(x+1)(y−1e+1)=0xy(x + 1)\left(y - \frac{1}{\sqrt{e}} + 1\right) = 0xy(x+1)(y−e​1​+1)=0

Choose the correct answer from the options given below:

Official previous-year question

Held on 15 May 2025 · Verified 13 Jul 2026.

Options

  1. A

    (C) and (D) only

  2. B

    (A) only

  3. C

    (B) only

  4. D

    (C) only

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