Disconnect, dislike, dishearten, disabled but dyslexia, dysphasia, dyspepsia.
These two prefixes, dis- and dys- seem to have very similar meanings - making a word negative. But it's a little more complicated than that.
Dis (from Latin, meaning apart) is much more common, so if you're not sure use this (dis). It makes a word negative, such as dislike. Or it can mean to reverse something: like disconnect
Dys-, on the other hand, comes from Greek and so is almost always used for medical or scientific words. It means bad or abnormal. So if you have dyspepsia you are not digesting your food well, people with dyslexia have some problems with language.