Problem 2

Show that the density distribution of [equation (4.5)] is a solution of equations (4.1) and (4.3).

Figure 4.1: Radial density distribution. A spherical cloud (left) and a cylindrical cloud (right). In the right panel, solutions for polytropic gases with $\Gamma =1.1$ (relatively compact) and $\Gamma =0.9$ (relatively extended) are plotted as well as the isothermal one.