How did the suffering of Gautama Buddha arise or co-arise?

I think I have found one answer to the question in Manual of Buddhism by Hardy Spencer. I quote from p.364:

The body of Budha was subject to pain and disease, and it was argued by the king of Sagal that on this account he could not be the all-wise. But Nagasena replied that there are various causes of disease, of which the karma of previous births is only one. All the pain felt by Budha was from some present cause, or from the contrivance of others. Thus the harvest may be poor, from the badness of the seed, without any fault whatever on the part of the husbandman. When a stone is thrown into the air, it falls on the ground, not from any previous karma, but naturally, from a cause then present. The purest vessel may have poison put within it. And when the earth is cleared and ploughed, it is not from any previous karma that it is thus lacerated, nor from any appointment of its own ; but from the will of another. In like manner, the pain felt by Budha was without any cause on his part ; it came naturally from some cause then present, or from the contrivance of some other person. {Milinda Prasna.)

Nagasena says that the pain felt by Budha was without any cause on his part. It came naturally from some cause then present or from the will of some other person.

Karma action driven by intention which leads to future consequences.

Buddha had already achieved enlightenment what good was to stay any longer? It was his time.Many people ask why the enlightenment one,did not see that the food was poisoned,simply that was his time,his karma,and he had no reason to stay.

He already had shown the way to end suffering,he achieved his purpose.Same as the others after him:Milarepa,Padmasambhava ect...

Now its up to us weather to follow them or not.

In the Pali suttas, the word 'dukkha' is used in three contexts, namely:

1. Painful feelings (dukkha vedana)

2. Unsatisfactory characteristic (dukkha lakkhana) of impermanent things

3. Suffering of attachment to or taking the five aggregates as one's own (pañcupādānakkhandhā dukkhā).

Only the suffering of attachment is real dukkha. The suffering of attachment is the only dukkha a Buddha can overcome. Therefore, when the Buddha had the deadly illness with painful feelings, this was not suffering. There is the phrase: "Pain is inevitable, but suffering is optional".

Many many suttas explain this, such as MN 37, the end of MN 38, SN 22.1, AN 8.6 & SN 36.6.

On touching a tangible with the body, he does not lust after it if it is pleasing; he does not dislike it if it is unpleasing. He abides with mindfulness of the body established, with an immeasurable mind, and he understands as it actually is the deliverance of mind and deliverance by wisdom wherein those evil unwholesome states cease without remainder. Having thus abandoned favouring and opposing, whatever feeling he feels, whether pleasant or painful or neither-painful-nor-pleasant, he does not delight in that feeling, welcome it or remain holding to it. As he does not do so, delight in feelings ceases in him. With the cessation of his delight comes cessation of clinging; with the cessation of clinging, cessation of being; with the cessation of being, cessation of birth; with the cessation of birth, ageing and death, sorrow, lamentation, pain, grief and despair cease. Such is the cessation of this whole mass of suffering. MN 38

Therefore, when mere painful feelings arise from sense contact, it is not really correct to call this 'Dependent Origination' because 'Dependent Origination' is basically used for only the 12-condition formula.

"What, bhikkhus, is the Nibbana-element with residue left? Here a bhikkhu is an arahant, one whose taints are destroyed, the holy life fulfilled, who has done what had to be done, laid down the burden, attained the goal, destroyed the fetters of being, completely released through final knowledge. However, his five sense faculties remain unimpaired, by which he still experiences what is agreeable and disagreeable and feels pleasure and pain. It is the extinction of attachment, hate, and delusion in him that is called the Nibbana-element with residue left.

According to Itivuttaka 44 (above), an Arahant (including the Buddha) can still feel pleasure and pain.

And soon after the Blessed One had eaten the meal provided by Cunda the metalworker, a dire sickness fell upon him, even dysentery, and he suffered sharp and deadly pains. But the Blessed One endured them mindfully, clearly comprehending and unperturbed.

The suffering had indeed ended for the Buddha. That was why he was unperturbed by physical ailments. He feels pain but does not suffer from it.

In the Sivaka Sutta, the Buddha explains that not everything one feels is due to past karma becoming ripe:

"There are cases where some feelings arise based on bile. You yourself should know how some feelings arise based on bile. Even the world is agreed on how some feelings arise based on bile. So any brahmans & contemplatives who are of the doctrine & view that whatever an individual feels — pleasure, pain, neither-pleasure-nor-pain — is entirely caused by what was done before — slip past what they themselves know, slip past what is agreed on by the world. Therefore I say that those brahmans & contemplatives are wrong."

"There are cases where some feelings arise based on phlegm... based on internal winds... based on a combination of bodily humors... from the change of the seasons... from uneven care of the body... from harsh treatment... from the result of kamma. You yourself should know how some feelings arise from the result of kamma. Even the world is agreed on how some feelings arise from the result of kamma. So any brahmans & contemplatives who are of the doctrine & view that whatever an individual feels — pleasure, pain, neither pleasure-nor-pain — is entirely caused by what was done before — slip past what they themselves know, slip past what is agreed on by the world. Therefore I say that those brahmans & contemplatives are wrong."

In the story of Ven. Chakkhupala in Dhammapada 1, we find that it is possible for an Arahant to be blind due to past karma becoming ripe prior to Nibbana.

But since he was already blind, he does not suddenly become cured and starts to have vision because of Nibbana.

On one occasion, Thera Cakkhupala came to pay homage to the Buddha at the Jetavana monastery. One night, while pacing up and down in meditation, the thera accidentally stepped on some insects. In the morning, some bhikkhus visiting the thera found the dead insects. They thought ill of the thera and reported the matter to the Buddha. The Buddha asked them whether they had seen the thera killing the insects. When they answered in the negative, the Buddha said, "Just as you had not seen him killing, so also he had not seen those living insects. Besides, as the thera had already attained arahatship he could have no intention of killing and so was quite innocent." On being asked why Cakkhupala was blind although he was an arahat, the Buddha told the following story:

Cakkhupala was a physician in one of his past existences. Once, he had deliberately made a woman patient blind. That woman had promised him to become his slave, together with her children, if her eyes were completely cured. Fearing that she and her children would have to become slaves, she lied to the physician. She told him that her eyes were getting worse when, in fact, they were perfectly cured. The physician knew she was deceiving him, so in revenge, he gave her another ointment, which made her totally blind. As a result of this evil deed the physician lost his eyesight many times in his later existences.

So, we find that no new karma becomes ripe after Nibbana. But it is possible that the Arahant could feel pain due to other reasons.

At the same time, any chronic conditions caused by previous karma becoming ripe prior to Nibbana, do not suddenly disappear due to Nibbana.

But in all cases, the Arahant is unperturbed. He feels pain but does not suffer from it. That shows that the Arahant has risen above suffering.

In this resource about dependent origination, Mahasi Sayadaw says:

One who watches these present resultant processes effectively does not have craving that is rooted in feeling and so will put an end to the cycle of existence completely. In other words, the meditator watches every mental and physical phenomenon that occurs at the six sense-doors clearly in terms of its three characteristics. Through this effective practice of mindfulness, the meditator gains insight into the nature of the sense-objects and overcomes attachment to them there and then (tadaṅga), that is he or she overcomes it by opposing it with the knowledge that undercuts it. The cessation of attachment rules out the arising of the other phenomena, e.g. clinging, the process of becoming, birth, etc. After the this cessation through insight the meditator overcomes the latent attachment completely through cutting-off (samuccheda) when he or she attains the knowledge of the Noble Path. At this moment the other phenomena, e.g. clinging etc., also become totally extinct.

There is no teaching that says: “With the extinction of feeling, craving ceases to exist.” This is not surprising for even Arahants do not have any control over the feelings that arise from contact with the six senses.