How can I prove that every solution of x'= f(x) is trivial or regular?

timer Asked: May 12th, 2013

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How can I prove that every solution of x'= f(x) (x is a function from an open interval to R^n) is trivial or regular? NOTE Note that we have to prove that a solution of an ODE of this form hasn't singularities, except in the trivial solution. f is a C^1 class function. Regular in this context means f(x) different than zero for each x. Trivial in this context meansf(x)=0 for each x.

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