"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."
ODEs where the initial values of the dependent variable and its derivatives are given.
"An initial condition 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 the system evolves with time given the initial conditions of the problem."
"An initial value problem (IVP) is an ordinary differential equation together with an initial condition."
"An initial value problem is an ordinary differential equation."
"The initial condition specifies the value of the unknown function at a given point in the domain."
"Solving an initial value problem often involves modeling a system in physics or other sciences."
"The differential initial value equation specifies how the system evolves with time."
"An initial value problem (IVP) is an ordinary differential equation together with an initial condition."
"An initial value problem typically requires finding the solution to the differential equation that satisfies the specified initial condition."
"An initial value problem specifies the value of the unknown function at a given point in the domain."
"The initial condition specifies the value of the unknown function at a given point in the domain, aiding in the solution of the problem."
"The main focus of an initial value problem in multivariable calculus is to find a function that satisfies both the differential equation and the initial condition."
"Physicists and scientists frequently model systems by solving initial value problems."
"The term 'initial' in 'initial value problem' refers to the initial condition that specifies the value of the unknown function at a given point."
"An initial value problem typically has a single initial condition that helps determine the value of the unknown function at a specific point."
"An initial value problem provides information about how a system evolves with time based on the given initial conditions."
"Solving an initial value problem is crucial in modeling various systems within the fields of science and physics."
"An initial value problem combines a differential equation with an initial condition to determine the behavior of the system over time."