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Differential equation problem

  1. Oct 10, 2007 #1
    1. The problem statement, all variables and given/known data

    Find the general solution of x^2y" + xy' - y = 1/x

    2. Relevant equations

    m(m-1) +am + b = 0 to solve an Euler Cauchy equation

    3. The attempt at a solution

    a=1 b=-1

    m(m-1) -m -1 =0

    m^2 - 2m -1 = 0

    I just wanna know whether the first step is right. And once I find out the values of M, do I use variation of parameters to find the particular solution? Thanks
  2. jcsd
  3. Oct 10, 2007 #2


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    Staff Emeritus
    Science Advisor

    One obvious error: a= +1 here , not -1. Yes, you can use "variation of parameters". Also, because the right hand side is a power of x, you could use "undertermined coefficients" although it is slightly harder to "guess" the correct form for a particular solution in such an equation as compared to a "constant coefficients" equation. Finally, the change of variable u= ln(x) will convert this equation to a "constant coefficients" equation.
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