Astrophysics in a Nutshell Problem

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Homework Statement



Consider a hypothetical star of radius R, with density ρ that is constant, i.e. independent of radius. The star is composed of a classical, non relativistic, ideal gas of fully ionized hydrogen,
Find the the temperature profile (T(r))

Homework Equations


dT(r)/dr = ( (-3*L(r)*k(r)*ρ(r)) / (4∏*(r^2)*4*a*c*(T(r))^3)
so sorry this is written poorly

The Attempt at a Solution


So what I did is try and assume which of the values on the right side are constant so I could take them outside of the integral, but I'm not sure.Please explain principles and equations fully. I really want to understand this!
 
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Maybe you could state the problem?
 
Oh sorry. I thought I did!
I edited it. I says find the temperature profile (T(r))
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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