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Second order DE, reduction of order method?

  1. Oct 5, 2011 #1
    1. The problem statement, all variables and given/known data

    find general solution of x2y''-xy'-3y=0

    2. Relevant equations

    two solutions are given, y1=1/x and y2=x3

    3. The attempt at a solution

    i think this is a reduction of order question? the only theory i can find in my text for second order DE relates to constant coefficients, and obvioulsy these ones arent. anyone have some method for reduction of order? or am i going about this the wrong way?

    thanks
     
  2. jcsd
  3. Oct 5, 2011 #2
    hold up.... by superposition of homogeneous equations...

    with y1 and y2 solutions, then a general solution would just be y=c1(1/x)+c2(x^3) ??

    but that seems too easy...
     
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