# Riccati differential equation in Matlab

• May 26th 2011, 11:42 PM
halunke86
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?

halunke86
• May 27th 2011, 01:16 AM
halunke86
I've a possibility to calculate a numerical solution for the differential equation:

I create a function called deqex:

function dydx=deqex(x,y)
dydx = 1/(2*x^2*y-1)

in the main programm, I solved the equation with:

[x,y]=ode23('deqex',[0,100],1.856*exp(-1i*pi/3));

Now I have the problem that I don't know how to calculate the derivations of the solution at the point x=0

Can anybody help?