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Linear ODE solutions

  1. Mar 11, 2012 #1
    Hey,

    I have been trying to work out how to solve this example question I found in a recommended text,

    http://img715.imageshack.us/img715/5052/asdavm.jpg [Broken]

    Everywhere I've been reading starts with since y=eta(x) is a particular solution then y=eta(x) + u is a general solution, but the question doesn't state eta(x) as a particular solution, is that a problem?

    Anyway in this question is the way to go simply subbing in y = eta + 1/si then noting that all the lone eta components cancel since they are a solution themselves.

    But when I do that,

    I end up with something like

    [itex]\frac{dx}{d\Psi }=\left[ p(x)+2q(x)\eta (x) \right]\Psi (x)+\frac{q(x)}{{{\Psi }^{2}}(x)}[/itex]

    and I can't rearrange it to form the equation which si solves,

    any idea on what i've done wrong?
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Mar 11, 2012 #2

    tiny-tim

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    hey physicsjock! :smile:

    where did that dx/dψ come from? :confused:

    it should be -(1/ψ2)dψ/dx :wink:

    (and then you'll be able to multiply throughout by ψ2)
     
  4. Mar 11, 2012 #3
    ahah what a silly mistake I made!

    Thanks heaps!
     
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