BhG 4.1

syntax

śrī-bhagavān (the glorious Lord) uvāca (he spoke):
aham (I) imam (this) avyayam (unchangeable) yogam (yoga) vivasvate (to Vivasvant) proktavān (the one who declared), vivasvān (Vivasvant) manave (to Manu) prāha (he spoke),
manuḥ (Manu) ikṣvākave (to Ikṣvāku) abravīt (he spoke).

grammar

śrī-bhagavān	–	śrī-bhagavant 1n.1 m.; TP: śriyā yukto bhagavān iti – the Lord united with majesty (from: śrī – lustre, majesty, fortune; √bhaj – to share, to love, to rejoice, to worship, bhaga – a share, good fortune, opulence; -mant / -vant – suffix denoting one who possesses, bhagavant – who possesses opulence);
uvāca	–	√vac (to speak) Perf. P 1v.1 – he spoke;
imam	–	idam sn. 2n.1 m. – this;
vivasvate	–	vi-vasvant 4n.1 m. – to one who illuminates, who has rays, to the Sun (from: vi-√vas – to shine forth; -mant / -vant – suffix denoting one who possesses);
yogam	–	yoga 2n.1 m. – yoga, yoking, application, a means, one of the schools of Hindu philosophy (from:√yuj – to yoke, to join, to engage);
proktavān	–	proktavant (pra-√vac – to declare, to speak) PP 1n.1 m. – one who declared;
aham	–	asmat sn. 1n.1 – I;
avyayam	–	a-vyaya 2n.1 n. – unchangeable, imperishable (from: vi-√i – to go away, to disappear, vyaya – going away, changeable, expense);
vivasvān	–	vi-vasvant 1n.1 m. –one who illuminates, who has rays, the Sun (from: vi-√vas – to shine forth; -mant / -vant – suffix denoting one who possesses);
manave	–	manu 4n.1 m. – to Manu, to one thinking, to a person (from: √man – to think);
prāha	–	pra-√ah (to speak) Perf. P 1v.1 – he spoke (inflected only in Perf., other forms from: √brū);
manuḥ	–	manu 1n.1 m. – Manu, one thinking, a person (from: √man – to think);
ikṣvākave	–	ikṣvāku 4n.1 m. – to Ikṣvāku, the first ruler of the Sun dynasty, the descendants of Ikṣvāku ruling in Ayodhyā (from: ikṣu – sugar cane);
abravīt	–	√brū (to speak) Imperf. P 1v.1 – he spoke;

textual variants

imaṁ → evam (thus);
vivasvate → vivasvato (of Vivasvant);

Śāṃkara

yo’yaṃ yogo’dhyāya-dvayenokto jñāna-niṣṭhā-lakṣaṇaḥ sa sannyāsaḥ karma-yogopāyaḥ | yasmin vedārthaḥ parisamāptaḥ pravṛtti-lakṣaṇo nivṛtti-lakṣaṇaś ca gītāsu ca sarvāsv ayam eva yogo vivakṣito bhagavatā | ataeva parisamāptaḥ pravṛttiṃ vedārthaṃ manvānas taṃ vaṃśa-kathanena stauti śrī-bhagavān |

imam adhyāya-dvayenoktaṃ yogaṃ vivasvate ādityāya sargādau proktavān aham | jagat-paripālayitṝṇāṃ kṣatriyāṇāṃ balādhānāya | tena yoga-balena yuktāḥ samarthā bhavanti brahma parirakṣituṃ, brahma-kṣatre paripālite jagat paripālayitum alam | avyayam avyaya-phalatvāt | na hy asya samyag darśana-niṣṭhā-lakṣaṇasya mokṣākhyaṃ phalaṃ vyeti | sa ca vivasvān manave prāha | manur ikṣvākave sva-putrāyādirājāyābravīt

Rāmānuja

commentary under the verse BhG 4.3

Śrīdhara

āvirbhāva-tirobhāvāv āviṣkartuṃ svayaṃ hariḥ |
tattvaṃ pada-vivekārthaṃ karma-yogaṃ praśaṃsati ||

evaṃ tāvad adhyāya-dvayena karma-yogopāyaka-jñāna-yogo mokṣa-sādhanatvenoktaḥ | tad evaṃ brahmārpaṇādi-guṇa-vidhānena tattvaṃ padārtha-vivekādinā ca prapañciṣyan prathamaṃ tāvat parasparāprāptatvena stuvan bhagavān uvāca imam iti tribhiḥ | avyaya-phalatvād avyayam | imaṃ yogaṃ purāham vivasvata ādityāya kathitavān | sa ca sva-putrāya manave śrāddha-devāya | sa ca manuḥ sva-putrāyekṣvākave ‚bravīt

Madhusūdana

yadyapi pūrvam upeyatvena jñāna-yogas tad-upāyatvena ca karma-yoga iti dvau yogau kathitau tathāpi ekaṃ sāṅkhyaṃ ca yogaṃ ca paśyati sa paśyati [Gītā 5.6] ity anayā diśā sādhya-sādhanayoḥ phalaikyād aikyam upacarya sādhana-bhūtaṃ karma-yogaṃ sādhya-bhūtaṃ ca jñāna-yogam aneka-vidha-guṇa-vidhānāya stauti vaṃśa-kathanena bhagavān |

imam adhyāya-dvayenoktaṃ yogaṃ jñāna-niṣṭhā-lakṣaṇaṃ karma-niṣṭhopāya-labhyaṃ vivasvate sarva-kṣatriya-vaṃśa-bīja-bhūtāyādityāya proktavān prakarṣeṇa sarva-sandehocchedādi-rūpeṇoktavān ahaṃ bhagavān vāsudevaḥ sarva-jagat-paripālakaḥ sargādi-kāle rājñāṃ balādhānena tad-adhīnaṃ sarvaṃ jagat pālayitum | katham anena balādhānam iti viśeṣeṇena darśayati — avyayam avyaya-veda-mūlatvād avyaya-phalatvāc ca na vyeti sva-phalād ity avyayam avyabhicāri-phalam | tathā caitādṛśena balādhānaṃ śakyam iti bhāvaḥ |

sa ca mama śiṣyo vivasvān manave vaivasvatāya sva-putrāya prāha | sa ca manur ikṣvākave sva-putrāyādi-rājāyābravīt | yadyapi prati manvantaraṃ svāyambhuvādi-sādhāraṇo ‚yaṃ bhāgavad-updeśas tathāpi sāmpratika-vaivasvata-manvantarābhi-prāyeṇādityam ārabhya sampradāyo gaṇitaḥ

Viśvanātha

turye svāvirbhāva-hetor nityatvaṃ janma-karmaṇoḥ |
svasyoktiṃ brahma-yajñādi-jñānotkarṣa-prapañcam ||

adhyāya-dvayenoktaṃ niṣkāma-karma-sādhyaṃ jñāna-yogaṃ stauti imam iti

Baladeva

turye svābhivyakti-hetuṃ sva-līlā-
nityatvaṃ sat-karmasu jñāna-yogam |
jñānasyāpi prāy yan-māhātmyam uccaiḥ
prākhyad devo devakīnandano ‚sau ||

pūrvādhyāyābhyām uktaṃ jñāna-yogaṃ karma-yogaṃ caika-phalatvād ekīkṛtya tad-vaṃśaṃ kīrtayan stauti imam iti | imaṃ tvāṃ sūryāyāhaṃ proktavān | avyayaṃ nityaṃ vedārtahtvān naveyeti sva-phalādityavyabhicāri-phalatvāc ca | sa ca mac-chiṣyo vivasvān sva-putrāya manave vaivasvatāya prāha | sa ca manur ikṣvākave sva-putrāyābravīt