The correct solution of the differential equation dy/dx = (1+ x2)(1+y2)

tan-1(y) = -x + x3/3 + C tan-1(y) = 2x + x3/3 + C tan-1(y) = x + x3/3 + C tan-1(y) = x - x3/3 + C

tan-1(y) = x + x3/3 + C

given differential equation is dy/dx = (1+ x2)(1+y2) ⇒ dy/(1+y2) = (1+x2)dx Integrating both sides of this equation, we get ∫dy/(1+y2) = ∫(1+x2)dx ⇒ tan-1(y) = x + x3/3 + C