# Homework Help: System of odes any idea?

1. Nov 2, 2005

### mathphys

i know the solution to a system of trhee odes of the form

div(xy)= C1 (1)
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