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Kurtzenhouse

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Kurtzenhouse Region Grand Est Département Bas-Rhin Arrondissement Haguenau-Wissembourg Kanton Brumath Gemeindeverband Basse Zorn Koordinaten 48° 44′  N , 7° 48′  O 48.74 7.8069444444444 Koordinaten: 48° 44′  N , 7° 48′  O Höhe 126–179 m Fläche 3,58 km 2 Einwohner 1.049 (1. Januar 2016) Bevölkerungsdichte 293 Einw./km 2 Postleitzahl 67240 INSEE-Code 67252 Kurtzenhouse (dt. Kurzenhausen , Kurtzenhausen ) ist eine Gemeinde mit 1049 Einwohnern (Stand 1. Januar 2016) im Département Bas-Rhin in der Region Grand Est (bis 2015 Elsass) in Frankreich. Kurtzenhouse ist Mitglied der Communauté de communes de la Basse Zorn, benannt nach dem Fluss Zorn. Am 1. Januar 2015 wechselte Kurtzenhouse vom Arrondissement Strasbourg-Campagne zum Arrondissement Haguenau-Wissembourg. [1] Inhaltsverzeichnis 1 Geschichte 1.1 Mittelalter 1.2 Neuzeit 1.3 Bevölkerungsentwicklung 2 ...

Uniqueness of solutions of an IVP

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0 $begingroup$ I have a misunderstanding regarding a very common reasoning: Let's i.e. look at the IVP $dot x=f(x), x(t_0)=x_0$ with $f(x)=(x-1)(x-2)$ . Now, for $x_0in ]1,2[$ there can be made an argument that the solution always stays in between $]1,2[$ . The usual way to reason this is since otherwise there would be a point, let's say $t_1$ , such that $lambda(t_1)=1$ or $lambda(t_1)=2$ and that conflicts with the uniqueness of the solution since it would have an intersecting point with one of the constant solutions. But I don't understand this: The constant solutions don't even solve the IVP if $x_0in ]1,2[$ , so why is it a problem that those solutions intersect? Is the point here that a solution $lambda$ for the IVP $x(t_0)=x_0$ would then also solve the IVP with $x(t_1)=1$ whic...