CUET · MATHS · PYQ PAPER 2025
For the differential equation \(x \frac{d y}{d x}+3 y=x^2 \log _e x\) which of the following statements are TRUE?
(A) Product of order and degree is 1
(B) Integrating factor is \(x^3\)
(C) Integrating factor is \(3 x\)
(D) General solution is \(y=\frac{x^3}{36}\left(6 \log _e|x|-1\right)+C x^{-3}\), C is an arbitrary constant
Choose the correct answer from the options given below:
- A (A), (C) and (D) only
- B (A) and (B) only
- C (A) and (D) only
- D (A), (B) and (D) only
Answer & Solution
Correct Answer
(B) (A) and (B) only
Step-by-step Solution
Detailed explanation
Given differential equation: \(x \frac{d y}{d x}+3 y=x^2 \log _e x\) Standard form: \(\frac{d y}{d x}+\frac{3}{x} y=x \log _e x\) (A) Product of order and degree is 1 Order = 1 Degree = 1 Product = \(1 \times 1 = 1\) Statement (A) is TRUE. (B) Integrating factor is \(x^3\)…
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