Initial value problem

In the field of differential equations, an initial value problem (also called a Cauchy problem by some authors) is an ordinary differential equation together with a specified value, called the initial condition, of the unknown function at a given point in the domain of the solution. In physics or other sciences, modeling a system frequently amounts to solving an initial value problem; in this context, the differential initial value is an equation that is an evolution equation specifying how, given initial conditions, the system will evolve with time.An initial value problem is a differential equationFor a large class of initial value problems, the existence and uniqueness of a solution can be illustrated through the use of a calculator.A simple example is to solve y ′ = 0.85 y {displaystyle y'=0.85y}   and y ( 0 ) = 19 {displaystyle y(0)=19}  . We are trying to find a formula for y ( t ) {displaystyle y(t)}   that satisfies these two equations.