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Bounded solutions

  1. Mar 15, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the general solution of: y''+(1/x)y'=0
    and show that only constant solutions are bounded.

    2. Relevant equations



    3. The attempt at a solution

    integrating factor say a=e^(int(1/x)dr)=x
    so xy''+y'=0. so (xy')'=0
    integrate both sides: xy'=c (c is a constant)
    integrate again: y=cln(x)+d (d is a constant)

    but i dont know how to show that only constant solutions are bounded.
    Thank you
     
  2. jcsd
  3. Mar 15, 2009 #2

    tiny-tim

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    Hi sara_87! :smile:
    But you're there

    ln(x) is unbounded, isn't it? :wink:
     
  4. Mar 15, 2009 #3
    Oh right so this means only the solutions y=d can be bounded, right?
    Also, there's a similar question:
    find the general solution of: y''=0 and show that only constant solutions are continuous.

    general solution i found to be: y=cx+d (again c and d are constants)
    but in this case, why can only constant solutions be continuous?
     
  5. Mar 15, 2009 #4

    tiny-tim

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    dunno :confused:

    must be a misprint :redface:
     
  6. Mar 15, 2009 #5
    :)
    It's not a misprint.
    Never mind.
    Thank you.
     
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