# Problem of the Week #76 - November 11th, 2013

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#### Chris L T521

##### Well-known member
Staff member
Here's this week's problem.

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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:

#### Chris L T521

##### Well-known member
Staff member
No one answered this week's problem.