This text will expose the readers to the ideas of formulating difference differential equations (Chapman-Kolmogorov differential equations) and using ODE45 in MATLAB to solve them. Machine interference problem are very important in the operation of many production industry. Production machines are subject to fail or breakdown. When a machine fails or breaks down it is sent to a repairer (server) to be repaired. This is done to meet up production target and reduce loss of production in the system. Four models for the machine interference problems are examined in this work. These are Model 1: Machine Interference Problem With Unreliable Server, where the server can go on single and multiple vacations. Model 2: Machine Interference Problem With Reliable Server, where the server can also go on single and multiple vacations. Model 3: Single Server Machine Interference Problem With Additional Server For Long Queues under N policy vacations. Model 4: Machine Interference Problem With Threshold Recovery Policy And Server Vacations. The Chapman-Kolmogorov differential equations for the models are solved using ODE45 (Runge-Kutta algorithm of order 4 and 5) in MATLAB.