5
$\begingroup$

I build a model for our problem, but i cannot get a result from my model. Could anyone give me some idea to solve this formula: $aX+bX^2=e^{cX}$

Thx in advance!

  • 0
    What is $a$, $b$ and $c$? I assume those are constants and you want to solve for $X$? It seems unlikely that you can get closed formulas for $X$. other than in very special cases. For fixed $a$, $b$ and $c$ any standard numerical method for solving equations should suffice. (Newton's method, bisection, or some variant of those.)2012-05-22
  • 1
    Newton's method will converge for "most" values of $a,b,c$ but studying precisely each case could be time-consuming. You may start with $(a,b,c)=(1,1,1)$, the function is convex near its negative $0$, and use a homotopy method to reach all other values of $(a,b,c)$. Matlab or Mathematica will solve this for you efficiently too. I do not think there is an explicit solution in terms of roots exponentials and logarithms but I would be greatly interested if someone could point to possible proofs of this, perhaps using methods of differential algebra.2012-05-22

1 Answers 1