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First order differential equation question

  1. Jan 15, 2013 #1
    The problem is : dy/dx=(x(x^2+1))/4y^3 when y(0)=-1/√2
    This is my work so far:
    The answer from the textbook is y=-(√(x^2+2)/2)
    As you can see, my work will never equal the textbook answer when you put it in the y= stuff form. What did I do wrong?
  2. jcsd
  3. Jan 15, 2013 #2
    I got a slightly different answer than what you posted from the text

    [itex] y(x) = -\sqrt{\frac{1}{2}(x^2+1)}[/itex]

    and mathematica agrees with me, so perhaps a typo?

    Anyway, it looks like your on the right track, although go back through the integration, I think you may be off by a factor.
    Then apply the boundary condition to find the integration constant.
    And simplify the algebra down to the answer.
    Also be conscience of taking roots,
    [itex] y(x) = ±(stuff)^{1/4}[/itex]
    good luck
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