I have a set of ten dependent variables x1, x2 ... x10 and an independent variable t. The differential equations are of the form(adsbygoogle = window.adsbygoogle || []).push({});

d x1 /dt = f1(x1, x2... x10)

d x2 /dt = f2(x1, x2... x10)

........................

d x10 /dt = f10(x1, x2... x10)

where f1, f2 ...f10 are non linear functions of x1, x2....x10

I am not interested in solving these equations, all I want is to find constants of motion, ie some functions of x1, x2 ... x10 which do not depend on t. I can find two independent constants of motion just by inspection. I am hoping that there are more, but is there any systematic way to find them?

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# Coupled non linear ordinary differential equations.

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