I asked about Du'a in hard times.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

If any disaster or calamity befalls the Muslims, such as epidemics, floods, fear of the enemy's outrage, aggression, oppression or injustice, the Muslims are ordained to supplicate in Qunoot in the last Rak'ah of every obligatory prayer. Qunoot should be before the Rukoo' or after standing up from the Rukoo’. Here are some pieces of evidence regarding the Qunoot:

1. It is reported by Ahmad, Muslim, an-Nassa'i and Ibn Maajah, on the authority of Anas that the Prophet Muhammad supplicated Qunoot for one whole month, calling down the wrath of Allah upon some Arab tribes (Arabs from Banu Sulaym, Ri'l and Zakwaan), then he left it (didn't supplicate Qunoot anymore). Al-Bukhari reported that he supplicated with Qunoot when his reciters (those who memorized the entire Quran by heart) were killed (by Arab tribes, Banu Sulaym, Ri'l and Zakwaan), and that he was not more grieved of any incident as he was in this incident.

2. It is reported by Ahmad, Muslim, and at-Tirmithi, on the authority of Baraa' Ibn 'Aazib that Prophet Muhammad supplicated with Qunoot in Maghrib and Fajr prayer.

3. It is reported by Ahmed, and Abu Dawood on the authority of Ibn ‘Abbaas, who said: The Prophet supplicated with Qunoot continuously during a whole month in Thuhr, Asr, Maghrib, 'Isha, and Fajr at the end of the prayer. He (Prophet Muhammad) recited (Qunoot) after raising from Rukoo' in the last Rak'ah, and then he called down the wrath of Allah upon Banu Sulaym, Ri'l, Zakwaan and 'Ossayyah, and the companions were saying Ameeen.

4. Qunoot should be preformed in the last Rak'ah of Thuhr and 'Isha prayer, and in the Fajr prayer after saying: 'Sami’a Allaahu Liman Hamidah' (Allah hears the one who praises Him). The supplicant should pray for believers and curse infidels (Kuffar).

In case the Muslim is facing his own calamities or problems not the whole Ummah (Muslim nation), there are some various Athkaar that will help remove his troubles and grief. The Prophet said: “Indeed I know a word, if an anguished man says it, Allah will drive away his anguish and grief. It is the word of my brother Yunus (Prophet Yunus : {None has the right to be worshipped but You (Allah). Truly, I have been of the wrong-doers.} [Quran 21:87]

This Hadeeth is reported by at-Tirmithi from Sa'd Ibn Abu Waqqaas . It is also reported by at-Tirmithi fromAsmaa' Bint 'Umays, who said: “The Prophet said to me: “Shall I not teach you some words to say when you feel distressed: “Allaahu Rabbi, La Ushriku Bihi Shay'a (Allah is my Lord, and I do not associate anything with Him).
Besides, there is another Hadeeth reported by Ahmad and others on the authority of Ibn Mas'ood that the Prophet said:
“There is no one who is afflicted with distress or anxiety and says, 'Allaahumma inni ‘abduka wa ibnu ‘abdika wa ibnu amatika; naasiyati biyadika; maadhin fiyya hukmuka; ‘adlun fiyya qadhaa’uka, as’aluka bikullis-min huwa laka, sammayta bihi nafsaka, aw anzaltahu fi kitaabika, aw ‘allamtahu ahadan min khalqika, aw-ista’tharta bihi fi ‘ilmi al-ghaybi ‘indaka, an taj‘alal-Qur’aana al-‘Atheema rabee‘a qalbee, wa noora sadri, wa jalaa’a huzni, wa thahaaba hammi.” (O Allah! I am Your slave, the son of Your slave, the son of Your female slave. My forelock is in Your Hand; Your decision concerning me shall certainly come to pass; just is Your Judgment about me. I implore You with each Name of Yours, by which You named Yourself, or You taught to some of Your creatures, or You revealed in Your Book, or which You keep secret in the knowledge of the Unseen with You, to enliven my heart with the Quran and to render it the light of my chest, the remover of my distress and discomfort), except that Allah removes his distress and replaces his sadness with joy.” Someone asked: “O Messenger of Allah, should we learn these words?” He said: “Yes. Whoever hears them should learn them.” [Ahmad]
For more benefit, please refer to Fataawa 343300, 88282, 13277, and 213715.
Allah knows best.