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I am trying to understand the second law of Newton and to inspire my son to study physics. My maths are elementary and so I don't understand the intuitive explanation of this very important theorem by the wikipedia.

Could someone explain why this theorem is well posed for a first order equation and is violated for higher than second derivatives, considering that I am a layman?

sofky
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    Can you please point out the reference to the wikipedia article you were reading? – uniquesolution Apr 03 '17 at 06:39
  • @uniquesolution https://en.wikipedia.org/wiki/Picard%E2%80%93Lindel%C3%B6f_theorem It is the wiki article on the Picard theorem – sofky Apr 03 '17 at 06:42
  • This question deals with going from "First order ODE's have a 1 dimensional solution space" to "$n$th order ODE's have an $n$ dimensional solution space". – Mark Schultz-Wu Apr 03 '17 at 06:45
  • to get helpful answers you should definitely expand your question. it is unclear what exactly you are asking about, and you also seem to misunderstand the point of Picard's theorem – Bananach Apr 03 '17 at 07:41
  • @Bananach what is the point of the theorem? – sofky Apr 03 '17 at 07:59
  • to show that, under some assumptions, unique solutions of ODE exist, no matter their order. indeed, a higher order ODE can be rewritten as a first-order ODE in higher dimensions. using this trick, the initial condition of the high -dimensional first-order ODE turns into an initial condition for all derivatives up to order-1 of the higher-order ODE – Bananach Apr 03 '17 at 08:11

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