Solution of the differentiable equation `x=1+xy(dy/dx)+(xy)^2/(2!)(dy/dx)^2+(xy)^3/(3!)(dy/dx)^3+...` is

Solution of the differential equation (1+x)(dy)/(dx)-xy=1-x is

The solution of the differential equation (dy)/(dx)=2xy is

Solution of the differential equation x^(2)(dy)/(dx)-3xy-2y^(2)=0 is

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

The solution of the differential equation (dy)/(dx)=(xy+y)/(xy+x) is