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Homework Help: 2nd order ODE

  1. Oct 2, 2008 #1
    Supose y1 and y2 are a fundamental set of solutions to a second order ODE on the interval
    -infinity<t<infinity.
    How can I show that there is one and only one zero of y1 between consecutive zeros of y2.

    I really don't even know how to egin approaching this problem. Any direction would be greatly appreciated.
     
  2. jcsd
  3. Oct 2, 2008 #2
    only one zero of y1 between consecutive zeros of y2??? what do you mean by this statement?
     
  4. Oct 2, 2008 #3
    I believe that I mean if y1(x)=0 and y1(z)=0 then y2(a) must be equal to zero with x<a<z.

    In other words, y1 and y2 must alternate zeros as t varies.
     
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