In Islam, a Muslim has to wash after passing urine.
However - health-wise, certain people do have the problem of urine dripping in drops even just after several minutes of completing urination in the toilet. At times these people experience urine coming in drops while in solat.
For such persons, the ruling in Shari'ah is that he or she would fall under the category of "Ma'zur" i.e. an (excused) person.
For solat purposes, after performing wudhu and while performing solat, the dropping of urine does not invalidate the solat or the wudhu.