Solving differential equations?
- To: mathgroup at smc.vnet.net
- Subject: [mg112497] Solving differential equations?
- From: Zhiyong Shen <zshen2002 at yahoo.com>
- Date: Fri, 17 Sep 2010 06:42:56 -0400 (EDT)
Following are the two differential equations:
dx/dr = [a*(1-x^2+y^2)]/{r(r-1)]^(1/2)-2b*[r/(r-1)]^(1/2)*x - 0.0152*[r/(r-1)]^(1/2)*xy
dy/dr = -2a*xy/[r(r-1)]-2b*[r/(r-1)]^(1/2)*y + 0.0076*[r/(r-1)]^(1/2) *(1+x^2-y^2)
with initial conditions:
x(5.67)= - {a[br + (b^2*r^2 + a^2 + 0.000058*r^2)^(1/2)]}/(a^2 + 0.000058*r^2)
y(5.67)= -{0.0076*r[br + (b^2*r^2 + a^2 + 0.000058*r^2)^(1/2)]}/(a^2 + 0.000058*r^2)
where r is the independent variable, x and y are dependent variables to be solved, and a and b are constant parameters.
It would be a great help to me if someone could give me a suggestion on how to solve these equations.
Sincerely,
Shen