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Fun eode

  1. Apr 24, 2008 #1

    lurflurf

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    Homework Helper

    I have been looking though Ince (Ordinary Differential Equations), nice book.
    I enjoyed solving this problem:
    6) pp. 157
    Integrate the system
    x*x''-y*y''=0
    x''+y''+x+y=0
    [Edinburgh, 1909.]
    we may assume x and y are twice differentiable functions
    defined everywhere from reals to reals
    ' denotes differentiation

    I would be interested in the methods used by others.
     
  2. jcsd
  3. Apr 25, 2008 #2

    HallsofIvy

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    Well, my first reaction would be that yy"= xx" so x"= (y/x)y".
    Then x"+ y"+ x+ y= 0 becomes (y/x)y"+ y"= (y+x)y"/x= -(x+y) so y"= -x. Put that back into the original equation and we have x"= y. Differentiating twice more gives xIV= -x.
     
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