- Thread starter
- Moderator
- #1
- Jan 26, 2012
- 995
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:
Remember to read the POTW submission guidelines to find out how to submit your answers!
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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:
Remember to read the POTW submission guidelines to find out how to submit your answers!
