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Math Help - Homogeneous ODE

  1. #1
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    Homogeneous ODE

    Thanks...

    I got this homogeneous equation:

    (2.r - s)ds + (r - 2.s)dr = 0

    y = 2+s
    x = r-1

    Made this subtitution:

    t = r/s
    dr = s.dt + t.ds

    And got this:

    ds/s = (2-t).dt/tē-1

    The integration leads me to a complicated and large answer, is there any better options here?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Homogeneous ODE

    Quote Originally Posted by mafra View Post
    And got this: ds/s = (2-t).dt/tē-1 . The integration leads me to a complicated and large answer, is there any better options here?
    I don't know why do you say that is a complicated and large answer. With a similar substitution s=vr , I get \log |r|+\int \frac{2-v}{1-v^2}dv=C i.e., a simple integral.
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