  We introduce a special type of dissipative Ermakov-Pinney equations of the
form v_{\zeta \zeta}+g(v)v_{\zeta}+h(v)=0, where h(v)=h_0(v)+cv^{-3} and the
nonlinear dissipation g(v) is based on the corresponding Chiellini integrable
Abel equation. When h_0(v) is a linear function, h_0(v)=\lambda^2v, general
solutions are obtained following the Abel equation route. Based on particular
solutions, we also provide general solutions containing a factor with the phase
of the Milne type. In addition, the same kinds of general solutions are
constructed for the cases of higher-order Reid nonlinearities. The Chiellini
dissipative function is actually a dissipation-gain function because it can be
negative on some intervals. We also examine the nonlinear case
h_0(v)=\Omega_0^2(v-v^2) and show that it leads to an integrable hyperelliptic
case
