1. Jun 23, 2013 #1

   jya

   

   I know we can solve e^x=x by the Lambert W function, but is it possible to solve the following equation:
   
   a*(e^(2x)-e^x)+b*x=c
   
   in terms of a, b, and c.

    

   jya, Jun 23, 2013
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3. Jun 23, 2013 #2

   Simon Bridge

   

   Science Advisor

   Homework Helper

   Gold Member

   Welcome to PF;
   
   

   Solving for x given a,b,c you mean? That would be the intersection of a line with a quadratic in e^x... that is $$ e^{x}\left ( e^x - 1\right ) = mx+k$$ ...where ##m=-b/a## and ##k=c/a##.
   And you want to find x given m and k.
   That help?

    

   Last edited: Jun 23, 2013

   Simon Bridge, Jun 23, 2013
4. Jun 23, 2013 #3

   jya

   

   Thank you Simon. Yes. I am wondering if there is some special function can solve this problem, i.e. given the values of a,b,c (or m,k in your equation) I can find out the value of x without looking at the graph.
   

    

   jya, Jun 23, 2013

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