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Conte Riccati and Jakob Hermann

  1. Apr 2, 2016 #1
    1. The problem statement, all variables and given/known data

    Riccati sets y/x=q and then arrives at x^2*dq. This is his analysis of Jacob Hermann's differential equations criticised by Johannes Bernoulli (published in 1710).

    x*dy-y*dx is a constant and is equivalent to dt.

    I have understood everything except for the q-substitution.


    3. The attempt at a solution

    Well, I have tried several times but all my solutions are not correct. E.g. x*dx*(dq-q). I have no idea how he got this square. I am missing some clues.
     

    Attached Files:

  2. jcsd
  3. Apr 2, 2016 #2

    epenguin

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    Perhaps you would find a more recent textbook easier to work from. :oldsmile: Ideal is roughly 1900-1970, after that they get more difficult again.

    If I have understood right your missing thing is the standard formula for derivative of a quotient, one of the half-dozen practically learnt off by heart by most calculus students, see any calculus textbook:

    y/x = q

    dq = d(y/x) = (x dy - y dx)/x2

    His formula Is just given by multiplying dq = (x dy - y dx)/x2 by q2
     
  4. Apr 2, 2016 #3
    Oh dear. What an idiot I am!!!!!!!!!!!!!!!!!!!!!!!! Many thanks. :)
     
  5. Apr 2, 2016 #4

    epenguin

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    Oh, I think when you have not done it for a year or two it fades. In fact, I am often not that sure whether to write x dy minus... or y dx minus... and have to stop and think about it.

    I was intrigued by your avatar, guessed who she was though I did not remember the name amongst all the Madame de's offhand, and traced her via Voltaire.
    I knew of Emilie du Chatelet's important translation of Newton, but I don't think I had known of her as the first to formulate of the law of conservation of energy.
    You are doing some interesting studies. :oldsmile:
     
    Last edited: Apr 2, 2016
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