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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 multivariable calculus, an initial value problem (IVP) is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the 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 th... Wikipedia