{{Short description|Type of calculus problem involving ordinary differential equations}}
In [[multivariable calculus]], an '''initial value problem'''<sup>[[#Notes{{efn|[Also called a] '''[[Cauchy problem]]</sup>''' by some authors.{{cn|date=December 2018}}}} ('''ivp''') is an [[ordinary differential equation]] together with an [[initial condition]] which specifies the value of the unknown [[function (mathematics)|function]] at a given point in the [[___domain of a function|___domain]]. Modeling a system in [[physics]] or other sciences frequently amounts to solving an initial value problem. In that context, the differential initial value is an equation which specifies how the system [[time evolution|evolves with time]] given the initial conditions of the problem.
== Definition ==
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==Notes==
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: <small>[a]</small> Also called a '''[[Cauchy problem]]''' by some authors{{cn|date=December 2018}}
