Homogeneous Differential Equation
A homogeneous differential equation is a type of differential equation in which all the terms are of the same order. In the context of first-order differential equations, a homogeneous equation can be written in the form:
dy/dx = f(y/x)
Homogeneous differential equations are called “homogeneous” because they can be transformed into a separable differential equation by a simple substitution, such as v = y/x.
Once the equation is transformed into a separable form, it can be solved using the separation of variables technique. Homogeneous differential equations have applications in various fields, including physics, engineering, and economics.