Need to solve first order non-linear differential equation

I need to solve first order non-linear differential equation to find the wave numbers of a Timoshenko beam for a certain slenderness ratio. I am actually trying to replicate the results of a paper.

Here is the code I have to do this:

%%%%%%

n1=1;

a0=1.875104068867879;

gamm=2.205;

syms a K real;

s = 1/K;

temp = a^2*(gamm^4+1)+s^2*(1+gamm^2);

b = sqrt(-temp+sqrt(temp^2-4*gamm^2*(gamm^2*a^4-a^2*s^2*(1+gamm^2))))/(sqrt(2)*gamm);

syms B real;

F1 = (a^2-B^2)*sin(a)*sinh(B)-a*B*(a^4+a^4*gamm^4+4*gamm^2*a^2*B^2+B^4*gamm^4+B^4)*cos(a)*cosh(B)/((B^2+gamm^2*a^2)*(a^2+gamm^2*B^2))-2*a*B;

dF1da = diff(F1, 'a');

dF1db = diff(F1, 'B');

dbdk = diff(b, 'K');

dbda = diff(b, 'a');

B = b;

dadk1 =eval(-dF1db*dbdk/(dF1da+dF1db*dbda));

f1=@(K,a) eval(dadk1);

%%The left boundary condition is undetermined for 0, so I can only put a %%number close to 0

for m=1:n1

     options=odeset('MaxStep',0.01);

    [K2,A(:,m)]=ode45(f1,[0.00001 0.4],a_bernoulli(m),options);

end

figure();

hold on;

grid on;

axis([0 0.4 0 12]);

for m=1:n1

    plot(K2, A(:,m));

end

%%%%%

thank you