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Nonlinear Differential Equation


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

about 0.6 and the period is about 3.7.

Much thanks in advance,


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