I learn Mathematica on my own, and use it on my scientific studies. Sometimes there are some well known commands, trivial features, or keywords that I don't know. I ask my questions to SE community and occasionally my questions are lousy due to my lack of mainstream knowledge. (Like that one.)
Should I erase those types of questions? or leave it on the site? What is the usual procedure for those (I thought it may broke the integrity or encourage another person to ask another lousy question).
In general, leave it on the site and let the community decide what to do with it. Closed questions can still be useful to people searching for answers. The system will automatically delete really bad questions after a while (see here).
Actually for the example you linked, I wouldn't consider it a lousy question at all. It was written clearly, properly formatted and had a meaningful title. Personally I wouldn't have closed it, but obviously there's a level of subjective judgement in deciding what is "easily found in the documentation".
NDSolve) would help. I doubt the answer is the best possible solution, although it's correct in theory. There might be a different solution for FEM than for the method of lines, for instance. It's potentially more interesting than it currently appears.