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 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:
    ∫4y^3dy=∫x(x^2+1)dx
    (y^4)/2=((x^2+1)^2)/2+c
    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: First order differential equation question
Loading...