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Differential equation

  1. Aug 31, 2010 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations



    3. The attempt at a solution

    The post I put up a while ago actually turns out to be the one above.

    So far I'm not getting the right answer, please help.
     
  2. jcsd
  3. Aug 31, 2010 #2

    epenguin

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    You can get everything involving x on one side, everything involving y on the other. Called 'variables separable'. Look up.

    Edit - just as was your previous one I have now seen which you did manage to do!
     
  4. Aug 31, 2010 #3
    Thanks.
    But on the way, 1/(1+x^2)dx = 1/(1+y^2)dy
    if I take an intergral, I get

    -1/(x+1) + c = -1/(y+1) + c

    This is 1/(x+1) + c = 1/(y+1) right?

    The answer states that y = (1+x)/[1+c(1+x)] -1

    I don't know how to get there.
     
  5. Aug 31, 2010 #4

    Dick

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    Right. You never really needed two c's. Just take your expression and use algebra to solve for y.
     
  6. Aug 31, 2010 #5
    Inverse both sides to find y+1, and then just subtract one from both sides to solve for y.
     
  7. Aug 31, 2010 #6
    from 1/(x+1) +c = 1/(y+1)

    that is y+1+c = x+1 right

    y(x) = x+c

    this is what I get, but the answer is quite different

    which is y = (1+x)/[1+c(1+x)] -1
     
  8. Aug 31, 2010 #7

    Dick

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    1 over 1/(x+1)+c isn't equal to (x+1)+c. Use correct algebra. Not just any algebra.
     
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