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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


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