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Reference.org
Initial value problem
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<p>In <a href="/facts/Multivariable_calculus/PEs5SgUF">multivariable calculus</a>, an initial value problem (IVP) is an <a href="/facts/Ordinary_differential_equation/ygKGQ8kD">ordinary differential equation</a> together with an <a href="/facts/Initial_condition/sA4ohFP4">initial condition</a> which specifies the value of the unknown <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> at a given point in the <a href="/facts/Domain_of_a_function/FQvoeUpX">domain</a>. Modeling a system in <a href="/facts/Physics/a7aH2y08">physics</a> 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 <a href="/facts/Time_evolution/8XxTc0fN">evolves with time</a> given the initial conditions of the problem. </p>