solving first order ode with initial value problem and root finding

I'm trying to solve this problem:

b=a*(1/(a^2*k^2))^0.5; which b is function of a,k

F=(b^6-a^6)*sin(a)*sinh(b)+2*a^3*b^3*cos(a)*cosh(b)-2*a^3*b^3;' which if F is function of b,a

i'm trying to solve this first ordinary equation da/dk=(-diff(f,b)*diff(b,k))/(diff(F,a)+diff(F,b)*diff(b,a) intial value a(0)=1.8

how can write this problem with matlab?

I’m trying to solve this first order ode problem with initial value problem. I want to plot “a” versus “k”. I want to use initial value problem and root finding method to solve this first order ode. I attached pdf file. I explain in this pdf file.

thanks