"Dx/dt" represents the rate of change of the variable x with respect to time, while "dy/dt" represents the rate of change of the variable y with respect to time. Essentially, they represent the derivatives of x and y, respectively, with respect to time.
The value "1-1/y" represents the instantaneous rate of change of y with respect to x. This means that for every unit increase in x, there is a corresponding decrease in the rate of change of y. This is also known as the inverse relationship between x and y.
This equation is nonlinear, as it contains variables with powers other than 1 and does not follow the form of a linear differential equation (where the dependent variable and its derivatives are only raised to the first power).
To solve this equation, we can use the method of separation of variables. This involves isolating the variables on opposite sides of the equation and then integrating both sides to find the solution.
This type of differential equation is commonly used in fields such as physics, engineering, and economics to model and analyze various real-world phenomena. It can be used to study rates of change, growth, and decay in systems that exhibit an inverse relationship between two variables.