Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook