A dynamical problem whose solution determines the state of a system at all times subsequent to a given time at which the state of the system is specified by given initial conditions; the initial-value problem is contrasted with the steady-state problem, in which the state of the system remains unchanged in time. Also known as transient problem.

An nth-order ordinary or partial differential equation in which the solution and its first (n - 1) derivatives are required to take on specified values at a particular value of a given independent variable.