Problems related to population growth constitute one of the most useful topics of applications of differential equations in management and microeconomics. Usually that sort of growth show exponential patterns, therefore it is linked to nonlinear models. Based on these aspects, the main aim of this study is the application of differential equations to a particular problem belonging to the field of management and ecological economics; it is the case of a growth pattern model evident in fish populations. This study contains a brief characterization of production functions, differential equations, and their levels of solution: (i) general; (ii) particular; and (iii) singular.