Ordinary Differential Equations/Higher Degrees

$$({dy \over dx})^n+F_1(x,y)({dy \over dx})^{n-1}+...+F_{n-1}(x,y)({dy \over dx})+F_n(x,y)$$

can theoretically be factored into

$$({dy \over dx}-r_1(x,y))({dy \over dx}-r_2(x,y))...({dy \over dx}-r_n(x,y))$$

Then any solution for the individual factors will be a solution to the whole equation. The general equation can be found to be the product of the solutions.