restart;

N={ F:=1, K:=1.2};

Eq:= diff(C(x),x$2)-F*diff(C(x),x)-F*K*C(x)=0;

Bcs:=  F*D(C)(0)=C(0)-1, D(C)(1)=0;

Sol:= dsolve(eval({Eq, Bcs}, N), [ C], numeric, output=listprocedure);

I changed the values of some parameters. See the solution below

Re_b.mw

Check this article it will be of help. HPM_and_VIM.pdf and the numerical solution is ham.mw