question_answer

The equation of the curve satisfying the differential equation \[y\left( x+{{y}^{3}} \right)\,\,dx=x\left( {{y}^{3}}-x \right)\,\,dy\]and passing through the point (1,1) is:

A)  \[{{y}^{3}}-2x+3{{x}^{2}}y=0\]    

B)  \[{{y}^{3}}+2x+3{{x}^{2}}y=0\]

C)  \[{{y}^{3}}+2x-3{{x}^{2}}y=0\]    

D)  \[{{y}^{3}}+2x-4{{x}^{2}}y=0\]

E)  None of these