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.