CUET · MATHS · PYQ PAPER 2023
The solution of the differential equation \(\cos x \sin y dx + \sin x \cos y dy = 0\) is:
- A \(\sin x - \sin y = C\), where C is a constant.
- B \(\sin x \sin y = C\), where C is a constant.
- C \(\cos x \cos y = C\), where C is a constant.
- D \(\sin x + \sin y = C\), where C is a constant.
Answer & Solution
Correct Answer
(B) \(\sin x \sin y = C\), where C is a constant.
Step-by-step Solution
Detailed explanation
\( \frac{\cos x}{\sin x} dx = - \frac{\cos y}{\sin y} dy \) \( \int \frac{\cos x}{\sin x} dx = - \int \frac{\cos y}{\sin y} dy \) \( \ln|\sin x| = - \ln|\sin y| + \ln|C| \) \( \ln|\sin x| + \ln|\sin y| = \ln|C| \) \( \ln|\sin x \sin y| = \ln|C| \) \( \sin x \sin y = C \)
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