Solving N set of equations with N+1 Unknowns

MATLAB Community,

I have been troubled by this problem. I don't have to find a numerical solution to the unknowns. All I want to do is find the other unknowns in terms of a single unknown. I tried using solve(eqn1,... eqnn,var1...varn) leaving the var n+1 as the one I want all the other variables to be defined with but the solution always shows 1x1 sym and when I try to read it the answer shows zero.

Kenneth

The following is my code I am trying to find A1,A2,B1,B2,C1,C2,D1,D2 in terms of w

clear
Y=62.9*10^9;
l=24.5*10^-3;
ls=1*10^-3;
h=300*10^-6;
b1=4*10^-3;
b2=6*10^-3;
d1=7800*b1*h;
d2=7800*b2*h;
I1=(b1*h^3)/12;
I2=(b2*h^3)/12;
d31=-1.74*10^-10;
s11=15.4;

syms A1 B1 C1 D1 A2 B2 C2 D2 x w;

digits(4);

U=10;

P1=(-(3*0.9*d31)/(s11*((1/b1)+(1/b2))))*U

P2=-P1;

ag1 = vpa(sqrt(-(P1/(2*Y*I1))+sqrt(((P1/(2*Y*I1))^2)+((d1*(2*pi*w)^2)/(Y*I1)))));

bg1 = vpa(sqrt((P1/(2*Y*I1))+(sqrt(((P1/(2*Y*I1))^2)+((d1*(2*pi*w)^2)/(Y*I1))))));

ag2 = vpa(sqrt(-(P2/(2*Y*I2))+sqrt(((P2/(2*Y*I2))^2)+((d2*(2*pi*w)^2)/(Y*I2)))));

bg2 = vpa(sqrt((P2/(2*Y*I2))+(sqrt(((P2/(2*Y*I2))^2)+((d2*(2*pi*w)^2)/(Y*I2))))));

def1=A1*cosh(ag1*x)+B1*sinh(ag1*x)+C1*cos(bg1*x)+D1*sin(bg1*x);

def2=A2*cosh(ag2*x)+B2*sinh(ag2*x)+C2*cos(bg2*x)+D2*sin(bg2*x);

A=vpa(def1);
A=subs(A, x, ls)

B=diff(def1);
B=subs(B, x, ls)

C=diff(def2);
C=subs(C, x, 0)

D=diff(def2,3);
D=subs(D, x, 0)

E=vpa(def1-def2);
E=subs(E, x, l)

F=diff(def1)-diff(def2);
F=subs(F, x, l)

G=vpa((Y*I1*diff(def1,2)))+(Y*I2*diff(def2,2));
G=subs(G, x, l)

H=vpa((Y*I1*diff(def1,3))+(P1*diff(def1))+(Y*I2*diff(def2,3))+(P2*diff(def2)));
H=subs(H, x, l)

S = solve(A, B, C, D,E, F,G, H,A1,A2,B1,B2,C1,C2,D1,D2)

[Walter Roberson]

Could you post the equations?