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Homework Help: Separable differential equation

  1. Apr 25, 2006 #1
    okay... i got this problem
    sovle the separable differential equation
    4x-2y(x^2+1)^(1/2)(dy/dx)=0
    using the following intial condition: y(0) = -3
    y^2 = ? (function of x)

    I guess that means the constant is -3

    so i put all the x on 1 side and all the y on one side

    4x = 2y(x^2+1)^(1/2)(dy/dx)
    (4x)(dx) = 2y(x^2+1)^(1/2)(dy)
    (4xdx)/(x^2+1)^(1/2) = 2ydy

    integral both sides I got
    4(x^2+1)^(1/2) = y^2

    i tried the following answers
    y^2 = 4(x^2+1)^(1/2)
    y^2 = 4(x^2+1)^(1/2)+9
    y^2 = 4(x^2+1)^(1/2)-3

    they are all wrong!!!

    WHAT IS WRONG?! IS MY WAY OF DOING IT TATALLY WRONG?!
     
  2. jcsd
  3. Apr 25, 2006 #2
    This is correct. [tex]y^2=4\sqrt{x^2+1}+C[/tex]

    Now plug in your initial condition to solve for C.
     
  4. Apr 25, 2006 #3
    well you got most of it but i dont know why you are trying 9 and -3 as c.

    it says y(0) = -3

    y = +-4*(x^2+1) + c

    so y(0) = +-(0^2+1) + c = -3

    can you figure it out from here
     
  5. Apr 25, 2006 #4
    if
    y^2 = 4(x^2+1)^(1/2)+c
    y = sqrt(4(x^2+1)^(1/2)+c)
    c = 5 is the correct answer.

    THANX!!!
     
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