Question: how to solve functional equation in maple

ha := (diff(c(t), t))/(c(t)*(diff(c(t), t))-c(t));
solve(subs(m=ha,f(m))*subs(m=subs(c(t)=a(t),ha)), f(m)) = subs(m=ha+subs(c(t)=a(t),ha), f(m), f);

just expect to find a function ?
 

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