Your mission, should you decide to accept it, is to compute the size and density of a solar mass white dwarf. The first step in your mission is to combine the three relevant equations into a single, second-order differential equation, known as the Lane-Emden Equation. The second step is to solve this equation numerically for the radius of the white dwarf, given a mass (assume one solar mass). After that, finding the density should be a piece of cake. The hand-out from class should help you through this homework with a minimum of pain. (No pain - no gain.)
The Lane-Emden Equation can be solved numerically for arbitrary adiabatic index, gamma. It can be solved analytically for gamma = 2 and gamma = 6/5. I will give you lots of extra-credit if you can derive either of these analytic solutions.
The numerical solution of the Lane-Emden Equation can presumably be found with the aid of Maple. However, I was not able to get a correct solution (w should cross zero for y between 3 and 4). If you can find out what is wrong with my Maple script, please let me know. Instead of Maple, I used a simple fortran program to compute the solution using a Runge-Kutta algorithm. If you are getting frustrated (as I was with Maple), you are welcome to borrow this code (also available in /ncsu/py228_info/polytrope.f).