have a difficult time doing sth和have difficulty doing sth是否都含有一个可以省略的in?

have a difficult time doing sth和have difficulty doing sth是否都含有一个可以省略的in?
我想问的是这个意思，have a difficult time中的time是不是和后面的doing有一定的同位关系，而后面的have difficulty后的doing却相当于时间状语，可以这样理解吗