Hi Yinka,
I took a look, and I have some questions. In the attached notebook you will see I did two things:
1) In the first step under your recursive solution section I looked at the equations 1, 9-12 you mention. The variable you say you are wanting to solve for do not appear. I suspect you type set them in the text, but use simpler forms for them in the Mathematica input. Could you clarify this?
2) In my second section, I build a rule set that sets all variables in your variable list to 1, and apply it to the equation set. There is a lot left, which I assume is entirely composed of the parameters. (exogenous variables). Does this look correct? Or are some of these typographic errors containing what should be variables.
I am still concerned about the cases in which variables appear both as factors and in exponents. These can be quite difficult. It may be that in that you will need to eliminate as many variables as you can, then solve a remaining system numerically, and then back substitute. This is perhaps good for some uses, but not very satisfying to a theoretician.
In[38]:= Solve[x Exp[x] + x == c, x]
During evaluation of In[38]:= Solve::nsmet: This system cannot be solved with the methods available to Solve. >>
Out[38]= Solve[x + E^x x == c, x]
In[39]:= Solve[Exp[x] + x == c, x]
During evaluation of In[39]:= Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >>
Out[39]= {{x -> c - ProductLog[E^c]}}
**** Yinka -- I just saw your post as I was writing this. Some is answered, but I thought I wold post anyway since some is not. For the exponent-type terms which do not contain any variable I suggest you assign them a simple symbol name. The less typesetting you do the better off you will be.
-- Best,
David
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