Initial Value Problem

An Initial Value Problem (IVP) is a way to find a specific solution to a differential equation, which describes how something changes over time or space. To do this, you need to know the starting point or initial condition, such as the initial temperature, position, or velocity at a given moment. With this starting information, you can determine how the system evolves. Essentially, an IVP combines a rule for change (the differential equation) with a starting situation, allowing you to predict future behavior uniquely.