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Solving a Partial Differential Equation

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

    Find functions y=y(x) defined on (-∞,0) or (0,+∞) which verify:

    xy'+(x2-1)cot(y)=0,
    y([itex]x_0{}[/itex])=[itex]y_0{}[/itex] for [itex]x_0{}[/itex]≠0 and cos([itex]y_0{}[/itex])≠0


    3. The attempt at a solution

    I'm really stuck on this one!
    Any help will be very much appreciated!
     
    Last edited: Apr 21, 2012
  2. jcsd
  3. Apr 21, 2012 #2

    tiny-tim

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    welcome to pf!

    hi the0! welcome to pf! :smile:

    hint: separation of variables? :wink:
     
  4. Apr 21, 2012 #3
    Ok, thanks!
    So I get:

    xy' = (1-2x2)cot(y)



    y'tan(y) = (1-2x2)/x

    Then how do I go about integrating the left hand side?
     
  5. Apr 21, 2012 #4

    tiny-tim

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    (where did that 2 come from? :confused:)

    easier if you write it with d's …

    tan(y) dy = (1-x2)/x dx :smile:
     
  6. Apr 21, 2012 #5
    I realised that it was that simple right after I posted it haha
    and I missed out the 2 in the original statement of the problem, my mistake, sorry about that.
    Thanks a lot!
     
  7. Apr 21, 2012 #6
    I realised that it was that simple right after I posted it haha
    and I missed out the 2 in the original statement of the problem, my mistake, sorry about that.
    Thanks a lot!
     
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