I would use "implicit differentiation". For example, differentiating the first equation, $u^2v- u= x^3- 2y^3$, with respect to x, wq have $2uv du/dx+ u^2 dv/dx- du/dx= 3x^2$. As "differentials in terms of the differentials of x and y" that would be $2uv du+ u^2 dv= 3x^2 dx$. Differentiating with respect to y would give $2uv du/dy- du/dy= 6y^2$ or, as "differentials", $2uv dv- du= 6y^2 dy$.