An *initial-value problem (or IVP)* is a [[Differential Equation|differential equation]] together with a point in its domain, known as an initial condition. > [!Example] > $\frac{d}{dx}y(x)=y(x), \quad y(3)=1$is an example of an [[Initial Value Problem for Scalar Ordinary Differential Equation]]. # Properties **Solution**: A solution to the initial value problem is a solution to the differential equation that satisfies the initial condition.