|Nov13-11, 06:11 PM||#1|
non-linear differential equation
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?
|Nov14-11, 05:12 AM||#2|
That's a common way to do it and you're left with:
taking square roots, separate variable again and get:
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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