While taking a course on engineering math, our professor explained that we need to see a partial differential equation to be able to determine the number and type of initial conditions we need with certainty, but didn't go on to explain why this is the case.
My question is that is there a generalized way (at least for a considerable number of PDEs) to determine the number and type of ICs and BCs we need to obtain a unique solution? I also know that for simple PDEs like heat ,wave and Laplace equations we can determine these conditions easily and might be tempted to generalize a hypothesis based on them, but I'm not sure that's the right thing to do.
If you know any reference which explains about these things, naming the articles or related theorems will be appreciated.