Translation:It usually does not affect my answer.
The difference is small. The main meanings of the two words are almost exactly the same. "Prøve" is "try" and "forsøge" is "attempt". The difference is similar to the difference between those two English words. "Forsøge" implies that you want to achieve something specific. "Prøve" can be used both when you are trying to achieve something and when you're just trying something. "Forsøge" sounds a little bit more formal. It suggests a slightly more complicated effort than "prøve", although "prøve" may also be used about complicated efforts.