question_answer

The solution of primitive integral equation \[({{x}^{2}}+{{y}^{2}})\,dy=xy\,\,dx\]is \[y=y(x).\] If \[y(1)=1\] and \[({{x}_{0}})=e,\] then \[{{x}_{0}}\]is equal to

A)  \[\sqrt{2({{e}^{2}}-1)}\]                     

B)  \[\sqrt{2({{e}^{2}}+1)}\]

C)  \[\sqrt{3}\,e\]

D)  \[\sqrt{\frac{{{e}^{2}}+1}{2}}\]            

E)       None of these