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Need help setting it up

  1. Jan 21, 2012 #1
    1. The problem statement, all variables and given/known data

    I cant figure out how to solve this problem. When i do it straight forward, I get a crazy complex equation. I think I need to play with it a little before I ∫ it, but I am not sure. Everything is real, and it is in my seperable diffy eg section

    dy/dx=(4x-4x^3)/(4-y^3)

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 21, 2012 #2

    Simon Bridge

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    So why not separate the variable like normal?
    [tex](4-y^3)dy = (4x-4x^3)dx[/tex]
     
  4. Jan 21, 2012 #3
    I did that and got
    4y-(4y^4)/4=2x^2-(x^4)/4+c.
    But I think that I need to make it y=F(x). I cant get the y by itself
     
  5. Jan 22, 2012 #4

    SammyS

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    That's pretty common with solutions to differential equations.
     
  6. Jan 22, 2012 #5
    I'm having a similar problem with simple DE's that are solvable via separation of vars or using an integration factor. Many problems come up with solutions containing y in the form of ye^y. My professor said that it's fine as the solution for her tests and so on, but in a real application, what would you do?
     
  7. Jan 22, 2012 #6

    Simon Bridge

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    In a real application you'd use it as the basis for a numerical solution.
    Note: ye^y is not the problem - it is that ye^y=f(x), and f(x) is the problem because it can be anything.

    When you can get one as a function of the other you have an analytic solution.
    There are a very large number of situations where you don't get one... in fact, for an arbitrary DE it is usually the case.

    working out whether an analytic solution exists is a tricky part of number theory.
     
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