# Ordinary Differential Equations/Higher Degrees

can theoretically be factored into

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.

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

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.

- This page was last edited on 27 November 2010, at 05:37.
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