Problem with solving system of equations using symbolic toolbox

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So my task is to figure out the constants named c1, c2 and c3 which are found in the f(r) function.
The relationship between these constants and my data is as follows:
We have the U1, U2, U3 and Ue functions.
We also have the L = U1+U2+U3-Ue;
U1, U2, U3, Ue and f(r) substituted into the L = U1+U2+U3-Ue function makes c1, c2 and c3 determinable by: @L/@c1 = 0 , @L/@c2 = 0, etc. (where @ makes for partial differentiation).
Now according to my problem and the way i am solving it, i should be getting a symbolic expression for c1,c2,c3 which i could use to suit the needs of my problem (that is my f(r) - a height function of a diaphragm- when set equal to say the given volume would produce the right results for the parameters I have an interest in).
The forum comes in to the part i am useless (and new) to this matlab environment. I give u the code this far:
syms r c1 c2 c3 V1 V2 z
b = 0.008;
a = b/2;
hp = 0.0004;
hpzt = 0.0002;
hb = 0.00002;
%b,hp,hpzt,hb in (m)
vb = 0.3;
vp = 0.23;
e33 = 15.031*10^(-9);
%e33, e11 in (F/m)
s11 = 16.4 * 10^(-12);
s12 = -5.75 * 10^(-12);
%s11 and s12 in (m^2/N)
v = -s12/s11;
d31 = -171 * 10^(-12);
%d31 in (C/N)
Ep = 160;
Eb = 5.17;
Epzt = 69;
%Ep,Eb in (GPa = 10^9 N/m^2)
neutralheight = 1/2 * (((Ep*hp^2)/(1-vp^2))+(Eb*(((hb+hp)^2)-hp^2))/(1-vb^2)+(Epzt*(((hpzt+hb+hp)^2)-((hp+hb)^2))/(1-v^2)))/(((Ep*hp^2)/(1-vp^2))+(Eb*hb/(1-vb^2))+(Epzt*hpzt/(1-v^2)));
h1 = hp+hb+(hpzt/2)-neutralheight;
f(r) = ((1-((4*r^2)/b^2))^2)*(c1+c2*(1-((4*r^2)/b^2)+c3*((1-((4*r^2)/b^2))^2)));
dfr = diff(f, r, 1);
df2r = diff(f, r, 2);
fi2 = (d31 / 4*d31^2 - 2*s11*e33*(1-v))*(df2r+dfr*(1/r));
fi1 = ((V1 - V2)/hp) - 2*h1*fi2;
U1 = ((pi*Ep*(((hp-neutralheight)^3)+ neutralheight^3))/3*(1-vp^2)) * int((r*df2r^2)+(2*vp*df2r*dfr)+(1/r)*dfr^2, r, 0, b/2);
U2 = ((pi*Eb*(((hp+hb-neutralheight)^3)+(hp-neutralheight)^3))/3*(1-vb^2))*int((r*df2r^2)+2*vb*df2r*dfr+(dfr^2)*(1/r), r, 0, a/2);
U3 = ((pi*(((h1+hpzt/2)^3)+(h1-hpzt/2)^3))/3*s11*(1-v^2)) * int((r*df2r^2)+2*v*df2r*dfr+(1/r)*dfr^2, r, 0, a/2) - ((2*pi*d31*(((h1+hpzt/2)^3)+(h1-hpzt/2)^3))/3*s11*(1-v)) * int((r*df2r + dfr) * fi2, r, 0, a/2) - (pi*d31*(((h1+hpzt/2)^2) + (h1-hpzt/2)^2)/2*s11*(1-v)) * int((r*df2r + dfr)*fi1, r, 0, a/2);
Ue = (pi*e33-((2*pi*d31^2)/(s11*(1-v))))* int(int(((fi1^2)+4*z*fi1*fi2 + 4*(z^2)*(fi2^2)*r), r, 0, a/2), z, h1-hpzt/2, h1+hpzt/2) + ((pi*d31)/(s11*(1-v))) * int(int((z*(fi1+fi2*2*z)*(df2r+(dfr/r))*r), r, 0, a/2), z, h1-hpzt/2, h1+hpzt/2);
L = U1+U2+U3-Ue;
f1 = diff(L, c1, 1);
f2 = diff(L, c2, 1);
f3 = diff(L, c3, 1);
This far, the result for f1 -which is c1 per se- comes as an expression that involves c2 and c3. The same goes for f2 and f3. How can i solve these three to get an answer for each one that doesnt involve the other two?
Thank you all in advance.

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