A homogeneous differential equation is a type of differential equation where all terms can be expressed as a function of the dependent variable and its derivatives. In simpler terms, if you can factor out a common variable from every term, the equation is considered homogeneous. These equations often have solutions that can be expressed in terms of a single function or a set of functions. Homogeneous differential equations are commonly encountered in various fields, including physics and engineering. They can be linear or nonlinear, and their solutions typically involve techniques such as substitution or the use of characteristic equations. Understanding these equations is essential for solving many real-world problems involving rates of change.