What is the ruling on making an open source(term used in technology world) product(software/hardware), but the money for the development of the product is from asking donations from peoples.Because its open source, people can benefit from it(the product) freely with some rules(if there is), so is this kind of asking included in prohibited asking?.

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 someone wants to make these hardware and software products to be open source and available for people to benefit from for free, there is nothing wrong with asking people to donate money for this purpose, and this is not considered begging (dispraised asking for money) but rather falls under the category of cooperation in righteousness.

However, if he wants to make these programs for the purpose of selling them and earning an income for himself, and people would still benefit from them in potential development, then in this case, asking people for money for this purpose falls under the category of asking for money that is deemed forbidden by the Sharee‘ah.

Al-Haafith Ibn Hajar underlined in Fat-h Al-Baari that begging for money is dispraised and mentioned some of the supportive evidence, like, for example, the verse wherein Allah, The Exalted, Says (what means): {An ignorant [person] would think them self-sufficient because of their restraint, but you will know them by their [characteristic] sign. They do not ask people persistently [or at all].} [Quran 2:273] The Prophet said: “A man continues to beg people for money persistently until he meets Allah without a shred of flesh on his face.” He also said: “Begging for money is impermissible except for three: a person who is smitten by extreme poverty, someone who has incurred a heavy debt burden, and a person whose property has been destroyed by a calamity that befell him...” He (Ibn Hajar) added: "Note: all the above applies to a person who asks for money for himself. As for a person who asks for money for the sake of others, it also appears that the ruling differs according to the relevant circumstances." [End of quote]

Allah Knows best.