A) \[y=x{{\sin }^{-1}}a+c\]
B) \[x=y{{\sin }^{-1}}a+c\]
C) \[y=x+x{{\sin }^{-1}}a+c\]
D) \[y=\,{{\sin }^{-1}}a+c\] where c is an arbitrary constant.
Correct Answer: A
Solution :
[a] \[\sin \left( \frac{dy}{dx} \right)-a=0\] \[\sin \left( \frac{dy}{dx} \right)=a\Rightarrow \frac{dy}{dx}={{\sin }^{-1}}a;dy={{\sin }^{-1}}adx\] Now, integrating both sides, \[\int{dy=\int{{{\sin }^{-1}}adx}}\] \[y=x{{\sin }^{-1}}a+c\]
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