Ongoing advancements in the design and fabrication of soft robots are creating new challenges in modeling and control. This paper presents a dynamic Cosserat rod model for a single-section 3D-printed pneumatic soft robotic arm capable of combined stretching and bending. The model captures the manufacturing variability of the actuators by tuning the pressure-strain relation for each actuator. Moreover, it includes a simple model of the pneumatic actuation system that incorporates the transient response of proportional pressure-controlled electronic valves. The model was validated experimentally for several quasi-static and dynamic motion patterns with actuation frequencies ranging from 0.2 Hz to 20 Hz. The model reproduced the quasi-static experiments with an average tip error of 4.83% of the arm length. In dynamic conditions, the average tip error was 4.33% for stretching and bending motions, 5.64% for five motor babbling experiments, and 22.53% for three challenging sinusoidal patterns. An ablation study of the model components found that the most influential factors for the average accuracy were gravity and strain gains, followed by damping and pressure transient. This work could assist researchers in focusing on the most significant aspects for closing the real-to-sim gap when modeling pneumatic soft robotic arms.