# Solving a system of equations with a specific shape of the solutions

I have a system of four equations, which are:

n=1;
U[r_] := (1 + r^2);
eq1 = uu'[r] + 1/r*uu[r] + I*n/r*vv[r] + k*ww[r] == 0;
eq2 = uu''[r] +
1/r*uu'[r] - ((n^2 + 1)/r^2 - k^2 + R*(k*U[r] - I*ω))*
uu[r] - I*2*n*vv[r]/r^2 - R*pp'[r] == 0;
eq3 = vv''[r] +
1/r*vv'[r] - ((n^2 + 1)/r^2 - k^2 + R*(k*U[r] - I*ω))*
vv[r] + I*2*n*uu[r]/r^2 - I*n*R*pp[r]/r == 0;
eq4 = ww''[r] +
1/r*ww'[r] - ((n^2 )/r^2 - k^2 + R*(k*U[r] - I*ω))*ww[r] -
R*uu[r]*U'[r] - R*k*pp[r] == 0;


The solution of the system are the functions {uu[r],vv[r],ww[r],pp[r]}. In this case, I want these functions has the shape:

uu[r_] := r^2*(S11 + S21*r^2 + S31*r^4);
vv[r_] := (S12 + S22*r^2 + S32*r^4);
ww[r_] := r*(S13 + S23*r^2 + S33*r^4);
pp[r_] := r*(S14 + S24*r^2 + S34*r^4);


So what I want to know is the value of the terms {S11,S21,S31,S12,S22,S32,S13,S23,S33,S14,S24,S34} which are all functions of {r,R,k,ω}

I tried to use Solve but doesn't works.

• How the dependent variables and S's are connected? – zhk May 5 at 3:17