So I'm confused on how we know we need x many BC and/or IC. For example, regarding the heat equation, we need 2 BC, and 1 IC (supposedly because there are two spatial derivatives and one time derivative). And similarly, for the Wave equation we need 2 BC and 2 IC. And another thing, why is it that when we look at D'Alembert's solution of the infinite string wave equation, why we only need 2 IC and no IC? Thanks, I'm very confused.