Separable Differential Equations

Definition

Separable differential equations are a type of differential equation that can be written in the form dy/dx = f(x)g(y), where f(x) and g(y) are functions of x and y, respectively. These equations can be solved by separating the variables and integrating each side separately.

Related terms

General Solutions: General solutions refer to solutions that include all possible solutions to an equation or problem. In the context of separable differential equations, finding the general solution involves including an arbitrary constant in the final solution.

Integration:

Integration is a mathematical operation that involves finding antiderivatives or definite integrals. In solving separable differential equations, integration is used to find the general solution by integrating both sides separately.

Initial Conditions:

Initial conditions are specific values given at a particular point in order to find a particular solution to a differential equation. When solving separable differential equations with initial conditions, these values are used to determine the specific constant(s) in the general solution.