Last updated on 21st Oct. 2018
The two poems are as follows (I have given below the transcript of his English translation of these poems):
1) Swami's declaration as Sai Avatar when he was 14 years old
Know that I am indeed Sai.
I am free from all the ties and bodily attachments.
None can fathom or understand my nature.
2) Swami's explaining his Avataric mission (in a letter to his elder brother Seshama Raju Garu, if I am not mistaken).
I have a task, a task to foster all mankind and ensure for all of them lives full of bliss.
I have a vow, a vow to lead all who stray from the straight path again into goodness and save them.
I am committed to the work that I love - to remove suffering of the poor and grant them what they lack.
My glory lies in protecting all those who worship and adore me with good conduct and steadfastness.
The hallmark of true devotion according to Swami is to treat the dualities like joy and grief, gain and loss with equanimity.
This is part of the video: "Prasanthi Vidwan Maha Sabha (Day 6) & Kavana Vijayam (Kavi Sammelan) Prasanthi Nilayam - 18 Oct 2018", https://youtu.be/uuTbjehl51o?t=1134 . I have set the starting time to 18 min. 54 secs which is when the Swami student and now faculty starts speaking about Bhagavan being the poet of poets. Then he speaks about these two Telugu poems of Swami and sings them with deep devotion and joy, and very melodiously. He also provides a translation in English. I thoroughly enjoyed the palpable devotion and joy, and the melodious singing of Bhagavan's powerful Avatar declaration and mission related Telugu poems (though I did not understand some of the Telugu) by Bhagavan's own student and now faculty.
He finishes this part at 22 min. 18 secs - i.e. a duration of 3 mins 24 secs. You may manually stop viewing the video here or watch other parts of his talk and later program involving notable Telugu poets.
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Please note that this Swami student and now faculty does not want his name to be shared. So I request those who recognize him to not mention his name in any comments they may put up on this post.