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Nonlinear Differential Equation

• To: mathgroup at smc.vnet.net
• Subject: [mg14142] Nonlinear Differential Equation
• From: David Djajaputra <dd4b at virginia.edu>
• Date: Mon, 28 Sep 1998 03:51:54 -0400
• Organization: University of Virginia
• Sender: owner-wri-mathgroup at wolfram.com

Hello,

I'm just wondering if anyone knows how to solve this DE:

y''(x) = - 2 y(x) / [1 - y^2(x)],   y(0) = 0,  y'(0) = 1.

The function is periodic. Mathematica says that it's transcendental but
it cannot solve it. I'm curious if the amplitude and/or the period can
be obtained in closed forms. By the way, if you plot it the amplitude
is

about 0.6 and the period is about 3.7.

Much thanks in advance,

David