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First order ODE with condition

  1. Aug 20, 2011 #1
    The question is x^2dy/dx + y^2=0 , y(1)=3

    I re-arrange the equation to get -1/y^2dy=1/x^2dx

    Seperated them, then I integrate both sides to get 1/y=-1/x + c

    Now I dont get how they got the answer y=3x/(4x-3), as when I try use the condition I get a different answer, could anyone help? I might have done something wrong in the integration?
  2. jcsd
  3. Aug 21, 2011 #2
    You just solve it for y: [tex]y=\frac{-x}{Cx+1}[/tex]. Then set y(1) equal to 3 (since that's the condition you're given) and solve (using good ol' algebra) for C: [tex]y(1)=\frac{-1}{C+1}=3[/tex]
    So, C=-4/3 and after you plug C into y, it is what your book says it is.
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