Initial Value Problem
An Initial Value Problem (IVP) is a type of differential equation that requires finding a function that satisfies the equation along with specific initial conditions. These conditions typically specify the value of the function at a particular point, allowing for a unique solution. IVPs are commonly encountered in various fields, including physics, engineering, and biology, where they model dynamic systems.
To solve an IVP, one often uses methods such as separation of variables, integrating factors, or numerical techniques. The goal is to determine a function that not only satisfies the differential equation but also meets the given initial conditions, ensuring that the solution is valid for the specified scenario.