Riccati differential equation in Matlab

Hello,

I have to solve the following differential equation:

$\displaystyle \frac{dy}{dx}=\frac{1}{2y^2x-1}$

or more exactly: i need the n-th derivation for x=0 as a function of the known value y(0)=y0.

I know (from Maple) that there is no explicit solution, just a implicit one.

Is there any possibility to calculate the implicit solution and additional the derivations of it in Matlab?

And I have a additional question:

The equation from above is an approximation of the following equation:

$\displaystyle e^{-i2\pi /3}\frac{H_{\frac{2}{3}}^{(2)}[\frac{1}{3}(-2\tau_s)^{\frac{3}{2}}]}{H_{\frac{1}{3}}^{(2)}[\frac{1}{3}(-2\tau_s)^{\frac{3}{2}}]}=\frac{1}{\delta \sqrt{-2\tau_s}}$

where H is the hankel function.

is there a way to calculate tau_s by a given delta?

Thanks for your help

halunke86