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Two ODE's

  1. Aug 19, 2010 #1
    Hi, friends :smile:.

    These are two equations, which were unable to resolve. Hope to help me. Note: this is not home, I just want to see how to resolve the equations. Thank answered.


    Find the common solution of the Euler's eqution:

    [tex](2x+1)^2y''-2(2x+1)y'+4y=0,[/tex] [tex]x>-\frac{1}{2}[/tex]
  2. jcsd
  3. Aug 19, 2010 #2
    Hello ferry2, I have solved your 2nd equation here:

    http://www.voofie.com/content/146/how-to-solve-2x12-y--2-2x1-y-4-y-0/" [Broken]

    And the solution is given by:

    [tex]y(x) = C_1(2x+1) +C_2 (2x+1) \ln (2x+1)[/tex]
    Last edited by a moderator: May 4, 2017
  4. Aug 19, 2010 #3
    Thanks a lot Ross Tang! Can you tell something about first equation?
  5. Aug 20, 2010 #4
    I tried various method in solving the 1st equation, but without any success. Sorry.
  6. Aug 20, 2010 #5
    Hello !

    May be a typo in the 1st equation ? No difficulty if (2x-y+1) instead of (2y-x+1).
    2nd equation : Let t=ln(2x+1) leads to
    d²y/dt² -dy/dt +y =0
    y(t) = exp(t)*(a*t+b)
    and y(x) according to ross_tang formula.
  7. Aug 20, 2010 #6
    It is possible there have been a typo. Thank you both.
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