This problem seem to be difficult for me, because i just know how to resolve simple linear differential equations in MATLAB?
$\left\{\begin{matrix} \ddot{z} = 2p + 3 & \\ p = \dfrac{1}{1+z}[1- pz\left(p^{-1.2} - p^{-1.3}\right)-3p\dot{z}]& \end{matrix}\right.$
If you write $w=\dot z$ then you get the system \begin{align} \dot w&=2p+3\\ \dot z&=w\\ 0&=(1+z) p - [1- pz\left(p^{-1.2} - p^{-1.3}\right)-3pw] \end{align} which is a differential-algebraic equation, in all probability of index $1$, as it has the form of an explicit index-1 system.
Thus you need to use one of the DAE solvers resp. DAE-capable ODE solvers that are presenton, in all probability of index $1$, as it has the form of an explicit index-1 system.
Thus you need to use one of the DAE solvers resp. DAE-capable ODE solvers that are present in Matlab.