A massive particle can indeed follow a straight path in a non-uniform electric field under certain conditions. Neutral particles, like atoms or neutrons, can easily achieve this trajectory. Charged particles can also follow a straight line if the electric field is appropriately configured, such as around a charged sphere. However, if the electric field has a non-zero curl, rectilinear motion becomes unlikely. Overall, the specific characteristics of the electric field play a crucial role in determining the particle's path.