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Separable D.E., Nonlinear in terms of y(x) after integration

  1. Dec 15, 2009 #1
    So, this is where I am stuck:

    [tex]ln\left(y\right)+y^{2} = \sin{x}+c_{0}[/tex]

    I am confrused... :blushing:
  2. jcsd
  3. Dec 15, 2009 #2
    Do you think that

    [tex]y(x) =\pm\sqrt{2LambertW(2exp(2sin(x)+C)}/2[/tex]

    is better?
    Last edited by a moderator: Dec 16, 2009
  4. Dec 15, 2009 #3


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    It's easier to express <x> in terms of <y>, wouldn't you say ?
  5. Dec 16, 2009 #4


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    EtherealMonkey, are you required to solve for y? That isn't always necessary or possible.
  6. Dec 16, 2009 #5
    hmm, but is it possible to make an explicit form in terms of x?
  7. Dec 16, 2009 #6
    kosovtsov just posted it....
  8. Dec 16, 2009 #7
    waw, lambert, i need to study that thing
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