How can i simplify the following symbolic equation in MATLAB?

I want to find this solution with solivng ode's.

The solution in the book is simplified with omega and lambda terms.

I have solved the differential equations and used the simplify command. However, my solution is very long and far from being similar with the book solution. How can i use the substitutions like omega and lambda in my solution?

My code:

syms phi(x) L Ex b0 h0 q G Ks w(x)
X= x/L;
b= b0*(1+X);
h= h0*(1+X);
I0= (b*h^3)/12;
Dxx= (Ex*I0);
Dphi= diff(phi,x);
fnc=Dxx*Dphi;
D2fnc= diff(fnc,x,2)== -q;
cond1= fnc(L)==0;
cond2= fnc(0)==0;
conds = [cond1 cond2];
fncSol(x)= dsolve(D2fnc,conds)

A0=b^2*h^2;
Axz= G*A0;
Dw= diff(w,x);
sol= Axz*Ks*(fncSol+Dw);
Dsol= diff(sol,x)==-q;



cond_1= w(L)==0;
cond_2= w(0)==0;
conditions = [cond_1 cond_2];
wSol(x)= dsolve(Dsol,conditions);
simplify(wSol(x))

[Torsten]

I miss the ODEs and boundary conditions that lead to the solution given by (5.4.23) in a mathematical notation.

Answer 1

[Dorukhan Gungor]