fixed points and stability of arcsin(x)

I'm analyzing a system of differential equations, and in one special case I just have

$$\frac{\mathrm dy}{\mathrm dt} = \arcsin(x)$$

Where $x$ is a whole mess of terms, that should be possible to collate into one term. I'm not sure how to analyze this.

I've tried some stuff so far, but I'm wondering if there's anything more to see here than the trivial result, $(0,0)$, when doing a stability analysis

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That whole mess of terms - do they involve only $t$ and constants? or do they also involve $y$? or what? –  Gerry Myerson Aug 17 '11 at 6:23
they don't involve $y$. the mess of terms is $$\frac{\omega_1 - \omega_2}{k_1 + k_2}$$ which is a difference in frequencies over a sum of coupling coefficients. –  rapidash Aug 17 '11 at 6:32
And there's no $t$ in there, right? –  Ｊ. Ｍ. Aug 17 '11 at 6:52

If that "whole mess of terms" does not depend on $t$ (as apparently it does not), then your equation is just $$\frac{dy}{dt} = \text{constant}.$$