1. ## Travelling wave solution

Hello, I'm hoping for some help with the following question.

Show that $u = \frac{1}{(1+exp[bz])^{2}}$ for b > 0 solves the following equation for a particular value of b:

$u'' + cu' + u(1-u) = 0$ where $u' = \frac{du}{dz}$ etc.

I've got to the following point and don't know where to go from here:
$(4-2b^{2}-2cb) + e^{bz}(6+2b^{2}-2cb) + e^{2bz}(4b^{2}+4) + e^{3bz} = 0$

This question's only worth about 7 marks out of 100 so I don't think it should take too long but I'm stumped!

Any help would be much appreciated