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Finding F(x)=G(x)+H(y)=K

  1. Sep 6, 2009 #1
    1. The problem statement, all variables and given/known data
    The differential equation dy/dx= 35/(y1/8+25x2y1/8 has an implicit general solution of the form F(x,y)=K. In fact, because the differential equation is separable, we can define the solution curve implicitly by the form F(x)=G(x)+H(y)=K.
    Find such solution and then give the related functions requested.


    2. Relevant equations



    3. The attempt at a solution
    dy/dx=35/(y1/8(1+25x2)
    1+25x2/35 dx=y1/8dy
    1/35[tex]\int1+25x^2 dx[/tex]=[tex]\int y^(1/8) dy[/tex]
    x+25x3/105=8/9y9/8
    105(8/9y9/8)-x-253=K
    so G(x)=x+25x3 and H(y)=8/9y9/8
     
  2. jcsd
  3. Sep 6, 2009 #2
    The problem is that this is incorrect and I dont know what I did wrong. Can someone see my mistake. Thank You in advance
     
  4. Sep 6, 2009 #3
    The bolded line is where you went wrong. Look carefully at what you did. It may be easier to see if you wrote it out "properly:"

    [tex]\frac{dy}{dx} = \frac{35}{y^{1/8} + y^{1/8}25x^2}[/tex]

    [tex]\frac{dy}{dx} = \frac{35}{y^{1/8}(1 + 25x^2)}[/tex]

    Edit: I'm assuming the bolded line really reads ((1+25x2)/35)dx=y1/8dy
     
    Last edited by a moderator: Sep 7, 2009
  5. Sep 6, 2009 #4
    So when I separate the variables it should be
    y1/8dy=[tex]35/1+25x^2 dx[/tex]
     
  6. Sep 6, 2009 #5
    Assuming you mean y1/8dy=(35/(1+25x2))dx, then yes, that is correct. It is more easily read as (35dx)/(1+25x2) or 35dx/(1+25x2) though, imo.
     
  7. Sep 6, 2009 #6
    Okay. Thank You
     
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