Equation for neutrons in a nuclear reactor

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Homework Statement
Neutron diffusion in nuclear reactor - deriving the equation of the slowing of the neutrons in momentum space and of their struggle to pass through the 238U resonance region without getting absorbed.
Relevant Equations
Boltzmann eq., Neutron transport eq., Neutron diffusion eq.
I am trying to solve a problem from Thorne and Blandford: Modern classical physics, chapter 3, problem 21: Neutron diffusion in nuclear reactor.
thorn_bland.JPG

I am struggling with how the equation, from which this should be calculated, should look like. I watched some videos where they did the derivation a such equation, however I don't know how to simplify it to fit my conditions. I think it should look roughly like this:
aaa.JPG

I'm not sure if there are supposed to be more terms or by what factors they should be multiplied, so is it somehow correct and I just need to add correct normalization, or am I completely wrong?
If someone could explain to me how to precisely create the equation from which I could get the desired relations, I would really appreciate it. Thanks!
 
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