NOTE. King Daśaratha remembered Rāmacandra while leaving his body. The Supreme Personality of Godhead has described the result of remembering Him while leaving this world:

NOTE. King Daśaratha remembered Rāmacandra while leaving his body. The Supreme Personality of Godhead has described the result of remembering Him while leaving this world:

anta-kāle ca mām eva smaran muktvā kalevaram
yaḥ prayāti sa mad-bhāvaṁ yāti nāsty atra saṁśayaḥ

“And whoever, at the end of his life, quits his body remembering Me alone at once attains My nature. Of this there is no doubt.” (Bhagavad-gītā 8.5)

One might object, “But Daśaratha offended Rāma and so it is not possible for him to have remembered Rāma at the moment of death.”

No. It is evident from the Rāmāyaṇa that Daśaratha had fully repented for his mistake of having agreed to banish Rāma. Śrīmad-Bhāgavatam notes that such repentence leads to direct perception of the Supreme Personality of Godhead:

yas tv atra baddha iva karmabhir āvṛtātmā
bhūtendriyāśayamayīm avalambya māyām
āste viśuddham avikāram akhaṇḍa-bodham
ātapyamāna-hṛdaye ’vasitaṁ namāmi

“I, the pure soul, appearing now bound by my activities, am lying in the womb of my mother by the arrangement of māyā. I offer my respectful obeisances unto Him who is also here with me but who is unaffected and changeless. He is unlimited, but He is perceived in the repentant heart. To Him I offer my respectful obeisances.” (Śrīmad-Bhāgavatam 3.31.13)

Through the history of Ajāmila also, Śrīmad-Bhāgavatam (6.1-3) illustrates that when one is fully repentent of his previous misdeeds and fully absorbed in devotional remembrance of the Supreme Lord, he is fully liberated from material existence at the end of that very life.