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No but if you have to just close the question and type it in again. Or if you want to see if you have already asked your question, type it into google and if the option of openstudy pops up, then there is your question that you asked. For example, copy and paste this question that I'm responding to right now into google and watch what happens.
Yes, there is no way to search it on the website but you can search within the website on google, if you type this into google:
[your search here] site:openstudy.com
It will return results from this website.
One reason we don't have the search is because the whole idea is to teach/learn so it's better to ask you question and learn how to find the answer rather than finding the question that has been asked and using their answer.