Non-linear differential equation

  1. 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?
  2. jcsd
  3. That's a common way to do it and you're left with:




    taking square roots, separate variable again and get:

    [tex]\frac{dv}{\sqrt{4k\sqrt{v}+c}}=\pm dt[/tex]

    That however looks kinda' messy to integrate although Mathematica gives a nice expression for the left side but then you get an implicit expression for v in terms of t:


    which is not solvable explicitly for v(t). Doesn't look like it anyway.
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