question_answer

The solution of the differential equation \[\frac{dy}{dx}+\frac{3{{x}^{2}}}{1+{{x}^{3}}}y=\frac{{{\sin }^{2}}x}{1+{{x}^{3}}}\]   is

A)  \[y\,\,(1+{{x}^{3}})=x+\frac{1}{2}\sin \,\,2x+c\]

B)  \[y\,\,(1+{{x}^{3}})=cx+\frac{1}{2}\,\,\sin \,\,2x\]

C)  \[y\,\,(1+{{x}^{3}})=cx-\frac{1}{2}\,\,\sin \,\,2x\]

D)  \[y\,\,(1+{{x}^{3}})=\frac{x}{2}-\frac{1}{4}\,\,\sin \,\,2x+c\]

E)  None of these