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For the differential equation x dy dx + 2y = x^2log_e x (A) Integrating factor is 2x (B) Integrating factor is x^2 (C) General Solution is y = x^2…

CUET UG 2025 — Mathematics Calculus

2025mcqmedium

For the differential equation xdydx+2y=x2log⁡exx\frac{dy}{dx} + 2y = x^2\log_e xxdxdy​+2y=x2loge​x

(A) Integrating factor is 2x2x2x

(B) Integrating factor is x2x^2x2

(C) General Solution is y=x216(4log⁡e∣x∣−1)+Cx−2y = \frac{x^2}{16}(4\log_e|x| - 1) + Cx^{-2}y=16x2​(4loge​∣x∣−1)+Cx−2 Where C is an arbitrary constant.

(D) General Solution is y=x416(4log⁡e∣x∣−1)+Cy = \frac{x^4}{16}(4\log_e|x| - 1) + Cy=16x4​(4loge​∣x∣−1)+C Where C is an arbitrary constant.

Choose the correct answer from the options given below:

Official previous-year question

Held on 3 Jun 2025 · Verified 13 Jul 2026.

Options

  1. A

    (A) and (C) only

  2. B

    (B) and (D) only

  3. C

    (B) and (C) only

  4. D

    (A) and (D) only

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