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Math Help - Riccati differential equation in Matlab

  1. #1
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    May 2011
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    Riccati differential equation in Matlab

    Hello,

    I have to solve the following differential equation:
    \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:
    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
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  2. #2
    Newbie
    Joined
    May 2011
    Posts
    2
    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?
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