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Homework Help: Euler's rule or Non-homogenous method?

  1. Jan 14, 2007 #1
    1. The problem statement, all variables and given/known data
    x^2 y' + xy + 5x^5=0

    2. Relevant equations
    no starting conditions

    3. The attempt at a solution
    cannot figure out how to do this. Euler's equations methods have no pure x terms, and the non-homogenous methods have some kind of separable thing, where the x terms neatly land up on RHs and y terms on LHS. But what do i do with this? Is it the polynomial expansion or maybe some kind of taylor series?
  2. jcsd
  3. Jan 15, 2007 #2


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    Science Advisor
    Homework Helper

    U can divide by "x" (assuming x different from 0) and then write the resulting eqn as

    [tex] (xy)'=-5x^{4} [/tex]

    Integrate both terms and then see what you get.

  4. Jan 15, 2007 #3
    I think dextercioby missed a term.

    Start by putting in the form y' + y*(1/x) = -5x^3

    Next, your integrating factor is p = e^[integral(1/x)dx] = e^(lnx) = x

  5. Jan 15, 2007 #4
    He didn't miss a term, your solution and his are identical, yours is just more detailed.
  6. Jan 15, 2007 #5
    Right :smile:
  7. Jan 15, 2007 #6
    Thanks all, was really helpful.
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