CUET · MATHS · PYQ PAPER 2025
The integrating factor of the differential equation \(x^2 \frac{d y}{d x}+x y=\log _e x\) is equal to :
- A \(e^x\)
- B \(e^{x^2 / 2}\)
- C \(x\)
- D \(\log _e x\)
Answer & Solution
Correct Answer
(C) \(x\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x} + \frac{1}{x} y = \frac{\log _e x}{x^2}\) \(P(x) = \frac{1}{x}\) \(IF = e^{\int P(x) dx} = e^{\int \frac{1}{x} dx} = e^{\log_e x} = x\)
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