(dydx)n+F1(x,y)(dydx)n−1+...+Fn−1(x,y)(dydx)+Fn(x,y){\displaystyle ({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
(dydx−r1(x,y))(dydx−r2(x,y))...(dydx−rn(x,y)){\displaystyle ({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.