# Solving Partial differential equation , distinguishing the meaning of boundary condition and Initial condition.

I have started my Differential equation course recently. And My professor was interchangeably using the term boundary condition and initial condition. I'm wondering what are the differences of their meaning in this context when dealing with the partial differential equations. I thought one would not need a boundary condition if a system extends to infinity, but the case of wave on a string would need, since it's a finite system For the initial condition, it always mean the initial state of the system. Can anyone tell me if my understandings are correct. Thank you!

So if $y(0)$ is given, in terms of time, that would be an "initial condition."
But if $y(0)$ and/or $y(L)$ are given for a differential equation that determines the temperature of a rod of length $L$, then $y(0)$ is more appropriately understood to be the "boundary condition" because it gives the temperature of the rod at the boundary of the rod.