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Homework Help: Problem with Sturm-Liouville equation

  1. Oct 31, 2006 #1
    Hi there :rofl: .
    I'm having troubles at a point in one Sturm-Liouville problem :grumpy: .

    I am trying to convert a generation eqn to the form of a Sturm-Liouville equation. The equation's form is as follows (where a(x),b(x),c(x),d(x) are arbitrary functions):

    a(x)y'' + b(x)y'(x) + [c(x) + (LAMBDA)d(x)]y(x) = o

    I begin by formatting in y'' + ... form. How do I proceed from here, please?


  2. jcsd
  3. Oct 31, 2006 #2
    If b(x) = a'(x) your equation is in Sturm-Liouville form...
  4. Nov 1, 2006 #3


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    If not, then you need to multiply by some [itex]\mu(x)[/itex] so that it is:
    a(x)[itex]\mu(x)[/itex]y'' + b(x)[itex]\mu(x)[/itex]y'(x) + [c(x) + ([itex]\lambda(x)[/itex])d(x)][itex]\mu(x)[/itex]y(x) = 0

    With a'[itex]\mu(x)[/itex]+ a[itex]\mu'(x)[/itex]= b(x)[itex]\mu(x)[/itex]. That gives you a simple differential equation for [itex]\mu(x)[/itex].
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