2xy(dy)/(dx)=x^(2)+3y^(2)

(x^(2)+xy)(dy)/(dx)=x^(2)+y^(2)

Solve (dy)/(dx)=(x^(2)+3y^(2))/(2xy)

The solution of the differential equation x=1+xy(dy)/(dx)+(x^(2)y^(2))/(2!)((dy)/(dx))^(2)+(x^(3)y^(3))/(3!)((dy)/(dx))^(3)+...is

(dy)/(dx)=(x^(2)-y^(2))/(xy)

(dy)/(dx) = (x^(2)+y^(2))/(xy)

x^(2)(dy)/(dx) = x^(2) - 2y^(2) + xy