A) (1, 2)
B) (2, 2)
C) (1, 1)
D) (2, 1)
E) (0, 1)
Correct Answer: C
Solution :
\[\sqrt{\sin x}(dx+dy)=\sqrt{\cos x}(dx-dy)\] \[\Rightarrow \]\[\sqrt{\sin x}\left( 1+\frac{dy}{dx} \right)=\sqrt{\cos x}\left( 1-\frac{dy}{dx} \right)\] \[\Rightarrow \]\[\frac{dy}{dx}(\sqrt{\sin x}+\sqrt{\cos x})=\sqrt{\cos x}-\sqrt{\sin x}\] \[\Rightarrow \]\[\frac{dy}{dx}=\frac{\sqrt{\cos x}-\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}\] \[\therefore \]Order =1, degree =1.
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