It was not narrated from the Prophet (peace and blessings of Allaah be upon him) or from any of his companions, as far as we know, that they used to raise their hands and say du’aa’ after praying an obligatory prayer. Hence we know that this is a bid’ah (innovation), because the Prophet (peace and blessings of Allaah be upon him) said: “Whoever does anything that is not in accordance with this matter of ours (Islam) will have it rejected.” (narrated by Muslim in his Saheeh, 3243). And he said: “Whoever innovates anything in this matter of ours (Islam) that is not part of it will have it rejected.” (Saheeh – agreed upon). 

However, reciting du’aa’ without raising one’s hands and without reciting it in unison is fine, because evidence to that effect was reported from the Prophet (peace and blessings of Allaah be upon him), indicating that he made du’aa’ both before and after prayer. The same applies to making du’aa’ after praying naafil prayers, because there is no evidence to indicate that this should not be done, even if one raises one’s hands, because raising the hands is one of the means of having one’s du’aa’ answered. But that should not be done all the time, rather only sometimes, because it was not reported that the Prophet (peace and blessings of Allaah be upon him) used to make du’aa’ raising his hands after every naafil prayer. All goodness rests in following the example of the Prophet (peace and blessings of Allaah be upon him) because Allaah says (interpretation of the meaning): 

“Indeed in the Messenger of Allaah (Muhammad) you have a good example to follow”[al-Ahzaab 33:21]

From Majmoo’ Fataawa wa Maqaalaat Mutanawwi’ah li Samaahat al-Shaykh Ibn Baaz (may Allaah have mercy on him), 11/168. 

See also Question no. 11543.