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Homework Help: Differential equation problem

  1. Dec 8, 2007 #1
    1. The problem statement, all variables and given/known data
    [tex]x^2\frac{dy}{dx}=\frac{2sqrt(y)}{x^4}[/tex]

    Where y(1)=3


    2. Relevant equations



    3. The attempt at a solution
    [tex]\int \frac{dy}{2sqrt(y)}=\int \frac{dx}{x^4}[/tex]

    [tex]4sqrt(y)=\frac{-1}{3x^3}+c[/tex]

    [tex]c=4sqrt(3)+\frac{1}{3}[/tex]

    So i end up with

    [tex]4sqrt(y)=\frac{-1}{3x^3}+4sqrt(3)+\frac{1}{3} [/tex]

    I'v gone wrong somewhere as the solution given does not match, i just can't spot where my mistake is. Thanks in advance for any help
     
  2. jcsd
  3. Dec 8, 2007 #2
    Hello,

    How'd you get [tex]\int \frac{dy}{2\sqrt{y}}=\int \frac{dx}{x^4}[/tex]
    from

    [tex]x^2\frac{dy}{dx}=\frac{2\sqrt{y}}{x^4}[/tex]?

    What happened to the [itex]x^2[/itex] term on the left?
     
  4. Dec 8, 2007 #3
    Sorry about that, stupid error. In the initial problem it should be [tex]\frac{2sqrt(y)}{x^2}[/tex]
     
  5. Dec 8, 2007 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Differentiate 4*sqrt(y). Do you get 1/(2*sqrt(y))?
     
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