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1st order differential equation

  1. Oct 21, 2008 #1
    It says find any solution y(x) of

    xy' = 1 + y^2

    I rearranged into seperable form to get

    dy/(1+y^2) = dx/x

    Integrated both sides to get

    arctan y = lnx + C

    then y(x) = tan(lnx + C)

    Is this ok? I'm a little struck on find 'any' solution for this, not too sure how else I could have done it.

    Perhaps I didn't do it correct?
  2. jcsd
  3. Oct 21, 2008 #2


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    Science Advisor
    Homework Helper

    I think you found all the solutions. If you want to find ANY specific solution then just set C=any constant. I'm not sure why you think you did something wrong.
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