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System of odes any idea?

  1. Nov 2, 2005 #1
    i know the solution to a system of trhee odes of the form

    div(xy)= C1 (1)
    xy grad(y) = -grad(z) -C1y (2)
    div(xy(y^2/2+ C2 z/x))=C3 (3)

    where x, y, and z are functions of r only, (spherical simmetry) and div F= (1/r^2) d (r^2F)/dr, and C1,C2 and C3 are constants, of course i know the solution
    when C1=C3=0 also.

    my problem is: i need to know the solution of an equivalent system for which (1) and (2) are identical to the ones above but now (3) is given by

    div(xy(y^2/2+C2 z/x))=C3 - f(y,z,r)

    My boundary conditions are
    that y(0)=0 and x(0)>0 and y(R)=C5 z(R)/x(R) in both cases, and i know the form of f. The systems of 3 odes is in reality a system of 2 because (1) can be inmediately integrated.


    I just want to know if there is a technique to construct a solution to the system with the modified equation (3) (including f) from the solution i know, i don't know , an equivalent to green functions for system of odes or something.

    Any help would be appreciated
    thanks
     
  2. jcsd
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