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Why does reduction of order work for linear ODEs?

  1. Nov 12, 2012 #1
    This is not a homework problem, I just want to understand some theory behind this mathematical method.

    Specifically, if we know that one solution is y1(t), then why is the second solution in the form

    y2(t) = v(t) * y1(t)?​

    Where v(t) is the function that you need to solve for. Why does this assumption always work?
     
  2. jcsd
  3. Nov 12, 2012 #2

    SammyS

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    The Wikipedia entry for reduction of order gives a good explanation.

    http://en.wikipedia.org/wiki/Reduction_of_order
     
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