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CUET · MATHS · PYQ PAPER 2023

The solution of the differential equation \(\cos x \sin y dx + \sin x \cos y dy = 0\) is:

  1. A \(\sin x - \sin y = C\), where C is a constant.
  2. B \(\sin x \sin y = C\), where C is a constant.
  3. C \(\cos x \cos y = C\), where C is a constant.
  4. D \(\sin x + \sin y = C\), where C is a constant.
Verified Solution

Answer & Solution

Correct Answer

(B) \(\sin x \sin y = C\), where C is a constant.

Step-by-step Solution

Detailed explanation

\( \frac{\cos x}{\sin x} dx = - \frac{\cos y}{\sin y} dy \) \( \int \frac{\cos x}{\sin x} dx = - \int \frac{\cos y}{\sin y} dy \) \( \ln|\sin x| = - \ln|\sin y| + \ln|C| \) \( \ln|\sin x| + \ln|\sin y| = \ln|C| \) \( \ln|\sin x \sin y| = \ln|C| \) \( \sin x \sin y = C \)