CUET · MATHS · PYQ PAPER 2025
Solution of the differential equation \(y \log _e y d x-x d y=0\) is (Where \(c\) is an arbitrary constant)
- A \(|y|=\left|c \log _e(x y)\right|\)
- B \(|x|=|c y|\)
- C \(|x|=\left|c \log _e y\right|\)
- D \(|y|=\left|c \log _e x\right|\)
Answer & Solution
Correct Answer
(C) \(|x|=\left|c \log _e y\right|\)
Step-by-step Solution
Detailed explanation
\(y \log _e y d x = x d y\) \(\frac{d x}{x} = \frac{d y}{y \log _e y}\) \(\int \frac{d x}{x} = \int \frac{d y}{y \log _e y}\) \(\log _e |x| = \log _e |\log _e y| + \log _e |c|\) \(\log _e |x| = \log _e |c \log _e y|\) \(|x| = |c \log _e y|\)
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