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Nonhomogeneous 2nd order dif equation

  1. May 18, 2014 #1
    Hello guys . I want to do nonhomogeneous 2nd order dif equation..I am trying to do this for 2 days , but I can't get good answer. Can you show me how to do this equation with constant variation method ( i know it best) or other I would be very gratefull , because after 2 days of trying I am surrendered... [itex]xy''-2y' = -\frac{2}{x^2} ; y(1)=-\frac{1}{3} ; y'(1)=1[/itex]
  2. jcsd
  3. May 18, 2014 #2


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    This is a first-order ODE for [itex]u = y'[/itex]: [tex]
    u' -\frac{2}{x}u = -\frac{2}{x^3}.[/tex] It has an integrating factor.
  4. May 18, 2014 #3


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    change variables
    ##\mathrm{u}(x)=x^{-2} \mathrm{y}^\prime (x)##
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