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Differential Equations Problem

  1. Jan 24, 2010 #1
    1. The problem statement, all variables and given/known data
    x y' + 3y = x2

    2. Relevant equations

    3. The attempt at a solution
    So I tried using an integrating factor (as I couldn't seperate variables).
    So I've said that the function p(x)= 1/x and q(x)=x. So the integrating factor is elog(x) or x. Putting this in:
    x y = [tex]\int x^{2}[/tex] so
    x y = [tex]\frac{1}{3} x^{3}[/tex] + c
    and finally: y(x) = [tex]\frac{1}{3} x^{2} + \frac{c}{x}[/tex] but this isn't the right answer. Where have I gone wrong?
  2. jcsd
  3. Jan 24, 2010 #2


    Staff: Mentor

    You don't have the right integrating factor. Starting from y' + (3/x)y = x, your integrating factor should be x3. Multiplying by the integrating factor gives x3y' + 3x2y = x4.

    This equation can be written as d/dx(x3y) = x4. Can you take it from there?
  4. Jan 24, 2010 #3
    ahh I see! yeah, that's great! thanks a load!
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