dehino ‘smin yathā dehe
kaumāraḿ yauvanaḿ jarā
tathā dehāntara-prāptir
dhīras tatra na muhyati

Translation of Bhagavad Gita 2.13

As the embodied soul continuously passes, in this body, from boyhood to youth to old age, the soul similarly passes into another body at death. A sober person is not bewildered by such a change.

Commentary by Sri A.C. Bhaktivedanta Swami Prabhupada of Gaudiya Sampradaya:

Since every living entity is an individual soul, each is changing his body every moment, manifesting sometimes as a child, sometimes as a youth, and sometimes as an old man. Yet the same spirit soul is there and does not undergo any change. This individual soul finally changes the body at death and transmigrates to another body; and since it is sure to have another body in the next birth—either material or spiritual—there was no cause for lamentation by Arjuna on account of death, neither for Bhishma nor for Drona, for whom he was so much concerned. Rather, he should rejoice for their changing bodies from old to new ones, thereby rejuvenating their energy. Such changes of body account for varieties of enjoyment or suffering, according to one’s work in life. So Bhishma and Drona, being noble souls, were surely going to have spiritual bodies in the next life, or at least life in heavenly bodies for superior enjoyment of material existence. So, in either case, there was no cause of lamentation.

Any man who has perfect knowledge of the constitution of the individual soul, the Supersoul, and nature—both material and spiritual—is called a dhira, or a most sober man. Such a man is never deluded by the change of bodies.

The Mayavadi theory of oneness of the spirit soul cannot be entertained, on the ground that the spirit soul cannot be cut into pieces as a fragmental portion. Such cutting into different individual souls would make the Supreme cleavable or changeable, against the principle of the Supreme Soul’s being unchangeable. As confirmed in the Gita, the fragmental portions of the Supreme exist eternally (sanatana) and are called kshara; that is, they have a tendency to fall down into material nature. These fragmental portions are eternally so, and even after liberation the individual soul remains the same—fragmental. But once liberated, he lives an eternal life in bliss and knowledge with the Personality of Godhead. The theory of reflection can be applied to the Supersoul, who is present in each and every individual body and is known as the Paramatma. He is different from the individual living entity. When the sky is reflected in water, the reflections represent both the sun and the moon and the stars also. The stars can be compared to the living entities and the sun or the moon to the Supreme Lord. The individual fragmental spirit soul is represented by Arjuna, and the Supreme Soul is the Personality of Godhead Sri Krishna. They are not on the same level, as it will be apparent in the beginning of the Fourth Chapter. If Arjuna is on the same level with Krishna, and Krishna is not superior to Arjuna, then their relationship of instructor and instructed becomes meaningless. If both of them are deluded by the illusory energy (maya), then there is no need of one being the instructor and the other the instructed. Such instruction would be useless because, in the clutches of maya, no one can be an authoritative instructor. Under the circumstances, it is admitted that Lord Krishna is the Supreme Lord, superior in position to the living entity, Arjuna, who is a forgetful soul deluded by maya.

Commentary by Sri Vishvanatha Chakravarthi Thakur of Gaudiya Sampradaya:

“One’s body becomes the object of affection as it is related to the soul (which is most dear to the self.) By relation with that body, one’s sons,   brothers or other relatives become objects of affection. And by relationship to them, even their sons also become objects of affection. So when their bodies perish, there will certainly be lamentation.”

In answer to this, he speaks this verse. “In the body belonging to the jiva (dehinah) one attains stages such as boyhood. After boyhood is destroyed one attains youth. When youth is destroyed one attains old age. In the same manner, one attains another body. Just as (yatha) one does not lament for the destruction of the objects of affection in the form of boyhood and youth of the body which are related to the soul, so (tatha) one should also not lament for the destruction of the object of affection, the body, which is also related to the soul.”

“But with the destruction of youth and attaining old age one does lament.”

“With the destruction of boyhood and attainment of youth one rejoices. With the destruction of worn out bodies of Bhisma and Drona, they will attain new bodies and will also become joyful.”

Another meaning is: Just as in one body one attains various states such as boyhood, the one jiva attains various bodies life after life.

Commentary by Sri Ramanuja of Sri Sampradaya:

2.13 As the self is eternal, one does not grieve, thinking that the self is lost, when an embodied self living in a body gives up the state of childhood and attains youth and other states. Similarly, the wise men, knowing that the self is eternal, do not grieve, when the self attains a body different from the present body. Hence the selves, being eternal, are not fit objects for grief. This much has to be done here; the eternal selves because of Their being subject ot beginningless Karma become endowed with bodies suited to Their Karmas. To get rid of this bondage (of bodies), embodied beings perform duties like war appropriate to their stations in life with the help of the same bodies in an attitude of detachment from the fruits as prescribed by the scripture. Even to such aspirants, contacts with sense-objects give pleasure and pain, arising from cold, heat and such other things. But these experiences are to be endured till the acts enjoined in the scriptures come to an end. The Lord explains the significance immediately afterwards:

Commentary by Sri Sridhara Swami of Rudra Sampradaya:

It may be argued that although it is certainly true that the Supreme Lord Krishna is not ever subject to birth and death being transcendental to the material manifestation what about the individual living entities who everyday are dying and being born. This is what is being answered in this verse. Even as the embodied living entity in the very same lifetime, possesses different physical bodies during different stages of life such as infancy, youth and old age; but always keeping the consciousness that one is the same individual despite these modifications presented in the form of the body. So it can be understood that on the destruction of the physical body the eternal soul is embodied in another physical body only due to the impressions one has accumulated in their subtle body and that the subtle body is real is observed at the birth of an infant who begins to suck the mothers breast immediately owing to past life impressions. The eternal soul does not perish when the physical body perishes; therefore the spiritually intelligent are not deluded by the birth or destruction of the body knowing that the eternal soul is not subject to birth or death.

Commentary by Sri Madhvacharya of Brahma Sampradaya:

This verse confirms that the soul is distinct from the body but by it being distinct does not make it independent. Only when the physical body is seen changing through infancy, childhood, youth etc. can this separate distinctness be perceived and thus confirmed until the soul giving up its present body acquires a new body and in some rare cases a living entity can recollect their past lives.

The physical body is obviously not what has the experience of childhood, youth, etc as is evidenced when the body is dead. The body is just the container and when the soul has departed. The body has no further identification with the soul leading itself to experience that it is a human being or tiger or worm or whatever physical form it possessed as the case may be. But due to the fact that the soul remains within the physical body during deep sleep similar to the ego centered mind; it is possible to perceive the existence of the soul as an independent consciousness whereas the body is merely like a wooden box.

This is verified by direct experience from the transcendental authority of the Vedas. It cannot be conceived by any mental or intellectual genius because it is beyond the scope of materialism. Nor can the Vedas reflect any vestige of human intellect or human endeavour within them because they come exclusively from the divine revelations of Krishna Dvaipayana Vyasa avatara an authorised incarnation of the Supreme Lord confirmed by name in the Vedic scripture known as Srimad Bhagavatam or Bhagavat Purana

Without understanding that there is a transcendental source to the eternal Vedas, the establishment of statements regarding righteousness cannot be applicable for all eternity and if they are not accepted for all time then there would have been no reason for them to exist and they would not have been the basic foundation for the instruction of righteousness. Without the universality of these premises the denial of what is not truth would not have been possible. There would then have been no connection to eternality from any established source. Therefore the principles found in the eternal Vedas constitute what is real. Otherwise without superior guidance from an eternal source nothing in this life can be accepted as absolute evidence. Things that we have heard would have no relevance as they would have nothing to reference it to. Otherwise one would have no thoughts or response to this that you are now reading. It would appear as a figment of the imagination. It would then be a cause of misery unless one was due to self-realisation an exception to this. If activities are judged with reference to righteousness or unrighteousness then facades of being unaware are not valid and intention is automatically exposed.

The transcendental statements found in the Vedas are eternal being established beyond the purview of time, hence the Vedas are self-evident and are to be known as absolute giving perfect knowledge of the Ultimate Truth. By the authority of the Vedas the wise are never deluded. Otherwise why would there be any sorrow thinking that the destruction of the physical body is the destruction of the soul. The soul cannot be destroyed. The soul is eternal thus the statement not that you were not. Not even by the destruction of the physical body. Hence the statement dehinah meaning the soul being the occupier of the deha which is the body. Even with the physical body changing its form as from infancy to childhood to youth etc. or being pitiful on account of old age etc. With the deterioration and demise of the body certainly comes the acceptance of another new body.

Now begins the summation.

The Supreme Lord Krishna to illustrate that there is no possibility of His having a physical body uses the word dehinah as an adjective to describe the plight of all embodied beings by stating: with the transmigration from one body to another. Therefore perceiving it as just a further modification of the body coming after old age there is no justification for sorrow.

Commentary by Sri Keshava Kashmiri of Kumara Sampradaya:

Because of the traditional conception that a son is born of a father and and that the grandfather died and also due to there being an injunction by the authority of the Vedic books of law that a brahmana remains impure during the ten days following a birth or death in his immeadiate family; how is it possible that one can think of the soul as being birthless and deathless? And if one continues to think of the soul as being born and of dying how can one alleviate their grief when the physical body dies? Can the authority of the Vedic books of law be denied? To clarify such doubts Lord Krishna uses the word dehinah meaning attributed to the embodied soul. It is the embodied soul who occupies the physical body which is the vehicle to experience the consequences of all ones actions. The embodied soul allocated a particular body experiences infancy, childhood, youth and old age, each stage of life which possess its own distinct attributes at different time periods. But although there is a difference in the stages and a difference in the perception of identity there is absolutely no difference in the soul. This is because although the activities one experiences continuously reside in the compartment of the memory and because when one is experiencing these different stages there developes the conception of identifying with the bodily designation in the form of it was I who in a young body played upon a fathers lap and was fed by a mother in infancy and it is I who now in an old body experience various relationships with children and grandchildren in old age. Only the bodily conception has changed the soul remains the same. In the same way that the embodied soul experiences the changing physical body, the embodied soul changes physical bodies at the time of death. There is no difference in the soul during any of these modifications of the physcical body and there is no difference in the soul due to the natural process of receiving another new body. One who is spiritually intelligent realizes that there is no birth or death associated with the soul and is not deluded by the apparent disfunctiong of the physical body even in the death of a son or father.

From this verse up until verse 30 beginning with dehi nityam avadhyo meaning the embodied soul can never be destroyed, the use of the singular is in the collective sense referring to all existing souls and this does not suggest that these embodied soul although of the nature of the Supreme Soul are on the same paltform with. This collectivity of the individual souls referred to is taught by the expert preceptor in the line of disciplic succession that the soul is eternal and never suject in any way to old age and death.

Statements supporting the varieagatedness of attaining communion with the Ultimate Consciousnes can be found in almost all of the chapters of Bhagavad-Gita and this variegatedness is supported based on the context by which they are written. Statements such as those of great virtue whose sins have been dissolved, those being freed from the delusion of the dualities, those great souls who possess the divine nature offer exclusive worship to the Supreme Lord, with their minds and lives surrendered to the Supreme Lord, those free from pride and infatuation, those who have conquered the vice of attachment and those whose desires have completely dissapeared, This varieagatedness is delieanated for those whose nescience is completely dissolved, whose doubts have been dispelled by knowledge, whose minds are firmly established in God, whose are righteously engaged in promoting the welfare of all living entities whose sins have been washed away, who are free from lust and anger, who have controlled their minds and who have realised the Ultimate Truth.

If this were not the case then accepting the conception of the oneness of all souls in all bodies would mean that we all would have a singular uniform experience. If we were all one soul then whether one were sleeping, another was waking and another fainting, all would experience the same sensations of pleasure pain simultaneously. Moreover there would be no difference in anyones perception due to the absence of any individuality and perceptions of you are and I am. But it is factually not like this in this world and this can be clearly understood by ones individual consciousness. Therefore it is established that those who propound oneness of the soul in all living entities are mistaken for even in the eternal soul there is also varieagatedness. So regarding death of the soul and other such fallacious arguements those with spiritual intelligence neither lament nor are deluded.
Commentary by Sri Adi Shankaracharya of Advaita Sampradaya:

2.13 As to that, to show how the Self is eternal, the Lord cites an illustration by saying,’…of the embodied,’ etc. Yatha, as are, the manner in which; kaumaram, boyhood; yauvanam, youth, middle age; and jara, decrepitude, advance of age; dehinah, to an embodied being, to one who possesses a body (deha), to the Self possessing a body; asmin, in this, present; dehe, body –. These three states are mutually distinct. On these, when the first state gets destroyed the Self does not get destroyed; when the second state comes into being It is not born. What then? It is seen that the Self, which verily remains unchanged, acquires the second and third states. Tatha, similar, indeed; is Its, the unchanging Self’s dehantarapraptih, acquisition of another body, a body different from the present one. This is the meaning. Tatra, this being so; dhirah, an intelligent person; na, does not; muhyati, get deluded.

Commentary by Sri Abhinavagupta of Kaula Tantra Sampradaya:

2.12-13 Na hi etc. Dehinah etc Never indeed did I not exist, but I did exist [always]. Likewise are you and these kings. If there can be lamentability for one, on attaining change in physical form then why is one not lamented over when one attains the youth from the boyhood ? He, who is wise, does not lament. But, wisdom is easily attainable for him whose concern is not even for this [present] body. Therefore you must seek wisdom.

dehino ‘smin yatha dehe
kaumaram yauvanam jara
tatha dehantara-praptir
dhiras tatra na muhyati

Sanskrit to English Word for Word Meanings:

dehinaḥ — of the embodied; asmin — in this; yathā — as; dehe — in the body; kaumāram — boyhood; yauvanam — youth; jarā — old age; tathā — similarly; deha-antara — of transference of the body; prāptiḥ — achievement; dhīraḥ — the sober; tatra — thereupon; na — never; muhyati — is deluded.