Sa se demonstreze ca ecuatia diferentiala \( \frac{dx}{dt}=\frac{1}{t^2+x^2} \) are solutie unica pe \( \mathbb{R} \) care satisface conditia initiala \( x(1)=1 \).
American Mathematical Monthly, 1988
ecuatie diferentiala are solutie unica
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Cezar Lupu
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ecuatie diferentiala are solutie unica
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
Ecuatia \( \frac{dt}{dx}=t^2+x^2 \) admite E.U.L. deci nu exista x a.i \( \varphi_1(x)=\varphi_2(x) \), deci nici solutiile ecuatiei initiale care sunt inversele \( \varphi_1^{-1} \) si \( \varphi_2^{-1} \) nu au nici un punct comun. Ramane de aratat ca \( \varphi \)e inversabila.
Last edited by dede on Tue Jan 22, 2008 11:47 pm, edited 1 time in total.
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Dragos Fratila
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