Given $ \bigg( \large\frac{dy}{dx}\bigg)^2$$+x=\large\frac{dx}{dy}$$+x^2$

$ \bigg( \large\frac{dy}{dx}\bigg)^2$$+x=\large\frac{1}{\Large\frac{dx}{dy}}$$+x^2$

Multiplying by $\large\frac{dy}{dx}$

$ \bigg( \large\frac{dy}{dx}\bigg)^3$$+\large\frac{dy}{dx}$$(x-x^2)-1=0$

Order = 1

Degree = 3