It is expected of/from you to find the solution.
Such rude behavior was not expected of/from you.
I am quite sure that from is the correct usage in both cases, but of could be used in the first one. Can somebody corroborate?
When you want to express the person who you expected would do something (as in the first example, and possibly the second too), one would normally use of. I would be inclined to say from is unidiomatic in your first sentence, especially because it is expected of you means "you are supposed/obliged to" here; where expected has this strong idiomatic sense of obligation, the agent should definitely have of:
It is expected of you to find the solution.
When it is not the person who you expect will do something, i.e. if the person has a different connection to the verb (like the indirect object below), you should not use of, but the appropriate preposition, as you no doubt know:
Such applause was not expected for our opponent.
If you use of here, it means that you did not expect our opponent to applaud like this. He becomes the agent:
Such applause was not expected of our opponent.
In your second example, the situation is less clear.
Such rude behavior was not expected of you.
The above is possible; it suggests to me that you were not supposed to exhibit such rude behaviour. But from is possible too, with a slightly different meaning:
Such rude behavior was not expected from you.
This means to me that we were surprised to see this behaviour from you. It does not suggest "you were not supposed to" in itself; but the context adds this sense of obligation at any rate (one is always supposed not to exhibit rude behaviour).
I would typically use "from" when referring to something I expect to receive from someone. Such as "a performance report is expected from everyone". Whereas when I'm referring to behavioral things that aren't "given" to anyone but "done" or "maintained", I would use "of". E.g. "attention to detail is expected of you."
However, I don't have any particular sources to corroborate that this IS indeed the rule. It just sounds more correct semantically to me.