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- Jan 26, 2012

- 995

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**Problem**: Let $g:\Bbb{R}\rightarrow\Bbb{R}$ be Lipschitz and $f:\Bbb{R}\rightarrow\Bbb{R}$ be continuous. Show that the system

\[\left\{\begin{aligned} x^{\prime} &= g(x) \\ y^{\prime} &= f(x)y\end{aligned}\right.\]

has at most one solution on any interval for a given initial value.

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**Hint**:

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