What is definition of initial value?

Initial value refers to the starting condition of a mathematical function or system at a specific point in time. It is a constant value or set of values that is used to determine the behavior of the function or system over time. In differential equations, initial value problems involve finding a solution to an equation that satisfies a set of initial conditions. These conditions specify the value of the function and its derivative at a specific point in time. The initial values are typically given as part of the problem and are used to determine the unique solution to the equation. In other words, the initial value is the value of a function at the beginning of a problem or experiment that helps determine how it will behave over time.