The general solution of the differential equation \(\displaystyle\frac{dy}{dx} = \frac{\cos x}{\sin y}\) is (C is an arbitrary constant)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\sin x + \cos y = C\)
The equation is variables separable:
\(\sin y\,dy = \cos x\,dx\)
Integrating both sides:
\(-\cos y = \sin x + C_1\)
Moving \(\cos y\) to the right and writing \(C = -C_1\):
\(\sin x + \cos y = C\)
Check by differentiating: \(\cos x - \sin y\,\frac{dy}{dx} = 0\), which gives \(\frac{dy}{dx} = \frac{\cos x}{\sin y}\).