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Solve non-linear differential analytically

  1. Nov 13, 2011 #1
    Hi,

    I am trying to solve the following equation analytically. I think the solution shouldnt be that hard but I'm really rusty on these kind of things.

    V' - k*V^-1/2 = 0

    where k is constant. Any help is appreciated, got to turn this in tomorrow!
     
  2. jcsd
  3. Nov 13, 2011 #2

    LCKurtz

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    Try separation of variables.
     
  4. Nov 13, 2011 #3
    ok I apologize I wrote that wrong. The original equation is:

    V'' - k*V^-1/2 = 0

    I then said u = V' therefore u' = u(du/dV)

    so the new equation is :

    u(du/dV) = V^-1/2*k

    Im a little rusty on separation of variables but I got a u in the final answer which means I have to integrate again since I need the final answer in terms of V.

    The goal is to prove k is proportional to V^3/2

    Am i doing this right?
     
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