Why Mathematica Can't Solve this Simple Equation

Questions
,
1

Dear All,

I have a rather simple equation and ask the software to solve it based on q. I need to have q based on other variables. I apply Solve[] but can not solve it and generates an Error!
Can any body help?

Thanks

In[8]:= Solve[(
  e^(-r t) y^-\[Alpha] (p q r y^\[Alpha] - 
     k q^\[Alpha] (r y \[Alpha] + 
        q (-1 + \[Alpha]) (1 + y \[Alpha]))))/q == 0, q]
During evaluation of In[8]:= Solve::nsmet:[u][i] This system cannot be solved with the methods available to Solve[/i][/u]. >>
Out[8]= Solve[(
  e^(-r t) y^-\[Alpha] (p q r y^\[Alpha] - 
     k q^\[Alpha] (r y \[Alpha] + 
        q (-1 + \[Alpha]) (1 + y \[Alpha]))))/q == 0, q]
2

Taking a look at your expression from your notebook, it is of the general form:

a q^(? - 1) + b q^? == 1

This generally will not have a closed form solution for arbitrary ?. The error message (actually an informative warning message generateted by Solve) is simply reflecting this fact.

(By the way, I am guessing that your e in your expression is meant to be the number E in Mathematica. But that is irrelevant to your question as those factors are overall factors in your expression and don’t affect the discussion.)

3

Thank you very much for the equation as well as the E.