Error using dsolve, any help would be greatly appreciated

Hi there, I'm having trouble using dsolve with symbolic functions; when I try to run I'm receiving an error stating:

"Warning: Explicit solution could not be found. 
> In dsolve (line 201)

    In VK3 (line 9) 

Error using sym/subsasgn (line 832)

Invalid indexing or function definition. When defining a function, ensure that the arguments are symbolic variables
and the body of the function is a SYM expression. When indexing, the input must be numeric, logical, or ':'."

Here's my code as it stands. I appreciate this may seem stupid to some, but I have relatively little experience with matlab, and if anyone would be kind enough to tell me where I'm going wrong, I'd be very greatful.

syms F(n) G(n) H(n)

c = 1.004e-6;

m = input('Angular Velocity = ');

z = linspace(0,20,20);

r = input('Radial Distance = ');

n = z*sqrt(m/c);

[F(n), G(n), H(n)] = dsolve(diff(F,2) == -G*2 + F*2 + diff(F)*H,...

      diff(G,2) == 2*F*G + H*diff(G),...

      diff(H) == -2*F,...

      F(0) == 0, H(0) == 0, G(0) == m*r, F(20) == 0, G(20) == 0);

U = m*r*F(n);

V = m*r*G(n);

W = sqrt(m/v)*H(n);

subplot(1,3,1)         

plot(U,n), xlabel('U'), ylabel('z'),...

      title('Radial Velocity Component')

subplot(1,3,2)      

plot(V,n), xlabel('V'), ylabel('z'),...

      title('Azimuthal Velocity Component')

subplot(1,3,3)         

plot(W,n), xlabel('W'), ylabel('z'),...

      title('Axial Velocity Component')

Answer 1

[RahulTandon]

%{
diff(F,2) == -G*2 + F*2 + diff(F)*H,...
    diff(G,2) == 2*F*G + H*diff(G),...
    diff(H) == -2*F,...
    F(0) == 0, H(0) == 0, G(0) == m*r, F(20) == 0, G(20) == 0
%}
%%SECTION 1
% REPHRASING YOU PROBLEM
syms z n m r c F(n) G(n) H(n)
c = 1.004e-6;
m = 200*pi  ; % sample value;                                              input('Angular Velocity = ');
r = 10000; % sample value;                                                   input('Radial Distance = ');

str1 = 'D2F ==-2*G + 2*F + H*DF';
str2 = 'DH == -2*F';
str3 = 'F(0) == 0';
str4 = 'G(0) == m*r';
str5 = 'F(20) == 0';
str6 = 'G(20) == 0';
str7 = 'D2G == 2*F*G + H*DG';
clc;
for z = linspace(0,20,20)
    n = z*sqrt(m/c);
    [F, G, H] = dsolve(str7,str1, str2, str3, str4, str5, str6,'n')
end

[RahulTandon]

Sorry, an explicit solution cannot be found