= Solution
For the <nonrelativistic white dwarf>, combine the <hydrostatic pressure support equation> and <enclosed mass> equation:
$$
\frac{dP}{dr}=-\frac{Gm\rho}{r^2},\qquad
\frac{dm}{dr}=4\pi r^2\rho.
$$
Eliminating $m$ yields
$$
\boxed{\frac1{r^2}\frac d{dr}\left(\frac{r^2}{\rho}\frac{dP}{dr}\right)=-4\pi G\rho,\qquad P=K_{\rm NR}\rho^{5/3}.}
$$
Introduce the <Lane-Emden variables for a stellar polytrope>,
$$
\rho=\rho_c\theta^{3/2},\qquad r=a\xi,\qquad
a^2=\frac{5K_{\rm NR}}{8\pi G}\rho_c^{-1/3}.
$$
The resulting <Lane-Emden equation> is
$$
\boxed{\frac1{\xi^2}\frac d{d\xi}(\xi^2\theta')=-\theta^{3/2},\qquad
\theta(0)=1,\quad\theta'(0)=0.}
$$
The <white dwarf> surface is at the first zero $\xi_1$ of $\theta$, with $R=a\xi_1$.
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