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Math Help - Solve these first order ODEs

  1. #1
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    Solve these first order ODEs

    I am doing these questions from the kreyszig textbook: http://i.imgur.com/atP9Oah.jpg

    For Q2, I did:

    y^3*y' + x^3 =0

    y^3 dy = -x^3 dx

    taking the integral of both sides

    y^4/4 = -x^4/4 + c
    y^4 = -x^4 + c

    Then I raised everything to 1/4 power.
    leaving us with y = +- (c-x^4)^1/4

    However, the wolfram also included an i and -i in front.
    Why is that?



    Additionally: I have no idea how to do Question 3. Any help would be appreciated.
    Last edited by 99.95; August 15th 2013 at 03:14 AM.
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  2. #2
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    Re: Solve these first order ODEs

    I've no idea about the Wolfram, but for Q3 separate the variables and then use the trig identity \cos^{2}A=\frac{1}{2}(1+\cos2A).
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  3. #3
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    Re: Solve these first order ODEs

    Quote Originally Posted by 99.95 View Post
    y^4/4 = -x^4/4 + c
    y^4 = -x^4 + c
    Note that the four fourth roots of 1 are 1, -1, i, -i.

    -Dan
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