How to find the coefficients of the following differential equation
Since this a homework type problem, only a few hints that should help you solve this problem yourself:


determine the transfer function of the first system by transforming the given differential equation and calculating $H_1(s)=W(s)/V(s)$.
do the same with the second system to obtain $H_2(s)=Z(s)/W(s)$.
from $Z(s)=V(s)$, determine $H_2(s)$ in terms of $H_1(s)$.