Initial value problem

An initial value problem is then a differential equation (ordinary or partial, or even a system) which, besides of stating the relation among the derivatives, also, by giving Initial Conditions, Specifies the values of the unknowns at some point.
This makes it possible to get a unique solution from the infinite
Number of potential ones. However, it shoshould be noted that not all
Possible choices of initial conditions specify a unique solution. It is
Also possible that there will be more than one solution satisfying
Particle choice of initial conditions, or perhaps no solution. In
Fact, one of
Main Problems in the theory
Of differential equations is to determine what sort of initial
Conditions will single out a unique solution of a given differential
Equation.