The solution of the differential equation `xy(dy)/(dx)={(1+y^2)(1+x+x^2)}/(1+x^2)` is:

Options

A. ` sqrt(1+y^(2))=Cxe^(tan^(-1)x)`
B. ` sqrt(1-y^(2))=Cxe^(tan^(-1)x)`
C. ` sqrt(1+y^(2))=Ce^(tan^(-1)x)`
D. ` sqrt(1+y^(2))=Cx`

Answer

a

Explanation

` xy (dy)/(dx) = (1 +y^(2)) (1+x/(1+x^(2)))`
` rArr y/(1+y^(2)) (dy)/(dx) = 1/x + 1/(1+x^(2))`
` 1/2 In (1+y^(2))= In x + tan^(-1) x In C`
` rArr sqrt(1+y^(2)) = Cxe ^(tan^(-1)x)`