Separability

Definition

Separability refers to the process of solving a differential equation by breaking it down into separate variables. This allows us to solve each variable individually and then combine the solutions to obtain the general solution of the differential equation.

Related terms

Initial Value Problem:

An initial value problem is a type of differential equation that includes an initial condition. It requires finding a solution that satisfies both the differential equation itself and the given initial condition.

Homogeneous Differential Equation: A homogeneous differential equation is one where all terms involving y (or any other dependent variable) can be factored out, resulting in an expression in terms of only x and y/y'.

Exact Differential Equation: An exact differential equation is one where there exists a function whose total derivative matches exactly with the given differential equation. This makes solving such equations easier as they can be written in terms of this function after certain manipulations.