280 Initial Conditions
A value of a function at a fixed point of its domain that is used to determine a unique solution of an equation.
definition [d] (Initial Condition) From Stewart: in many physical problems we need to find the particular solution that satisfies a condition of the form
- \(y(t_{0}) = y_{0}\) .
This is called an initial condition, and the problem of finding a solution of the differential equation that satisfies the initial condition is called an initial-value problem.
where
- \(y\) is the unknown function.
- \(t_{0}\) is a fixed value of the independent variable.
- \(y_{0}\) is the prescribed value of \(y\) at \(t_{0}\).