initial value problems

An initial value problem involves finding a specific solution to a differential equation that matches a known starting point. Imagine you know the rate at which a car is accelerating and the exact speed at the moment you start measuring. Using this starting point (initial condition), you can determine the entire journey’s speed or position over time. In math, the problem combines the differential equation (the rate of change) with the initial value (the known starting state) to uniquely describe how a system evolves from that starting point onward.