Initial value problem
= Initial value problem
{title2=$u(t_0)=u_0$}
{wiki}
An initial value problem specifies an <ordinary differential equation> together with the state at a starting time. For a continuous <linear differential equation> $u'=A(t)u$, every prescribed finite vector $u_0$ at $t_0$ determines a unique solution on the coefficient interval. This is different from a <boundary value problem>, which can prescribe values at distinct endpoints.