# System of differential equations - solving for a constant

I will reformulate my question in the hopes it will be more intelligible.

First, I defined the functions:

f1[r_] = b*SphericalBesselJ[l, α*r];
f2[r_] = c*SphericalHankelH1[l, I*β*r];

g1[r_] := D[f1[r], r]/(f1[r]);
g2[r_] := D[f2[r], r]/(f2[r]);


And I want to set:

f1[a]==f2[a]
g1[a]==g2[a]


Is it possible to use these two equations to find another equation that relates Alpha, Beta and a?

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?E gives E is the exponential constant E (base of natural logarithms), with numerical value \[TildeEqual]2.71828. >> so E can not be used as variable. May be that is the problem? – Nasser May 30 '14 at 7:19
I have changed to variable name to $N$ now. I am still getting the same response. – Thiago May 30 '14 at 7:25
I have changed to variable name to N now But N is also a Mathematica command. ?N (it is better to avoid all UpperCase first letter things when programming in Mathematica. – Nasser May 30 '14 at 7:30
And please correct all system symbols like E and N in text and in code. If symbol turns black color from blue and is not defined it means it is a system symbol. Do not use them for variables. – Vitaliy Kaurov May 30 '14 at 7:42
@Nasser I have completely reformulated the question now. I hope it is more clear. – Thiago May 30 '14 at 9:09