Initial value problem

The initial value problem (IVP) is a very common class of problem in Differential Equations.

As the name suggests, in an IVP, an initial value is given along with a differential equation.

$y(t_{0})=y_{0}$

For higher order ODEs, more than one initial value is needed to fully define a differential equation. These initial values must be at the same point (unlike in boundary value problems)