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I want to know that, is there any necessary and sufficient condition for a system of differential equation

$$ \frac{dx_i}{dt} = c_i f$$ where $f$ is a smooth function from $\mathbb R^n$ to $\mathbb R$ and $c_i$ are constant for $i=1,2...n$; to have a unique solution.

Thanks in advance.

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    I assume that $c_i$ are constant?2012-09-07

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