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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Oh sorry. I thought I did!
I edited it. I says find the temperature profile (T(r))