A problem has arisen. (Inidcating that a problem has appeared while it has not been existent before now)
Prices are rising. (This means that the prices were somehow high and now they are higher.)
According to Collins Cobuild Dictionary:
arise - rise
Both arise and rise are irregular verbs. The other forms of `arise' are arises, arising, arose, arisen. The other forms of `rise' are rises, rising, rose, risen.
When an opportunity, problem, or new state of affairs arises, it begins to exist. This is the most common meaning of arise.
He promised to help Rufus if the occasion arose.
A serious problem has arisen.
When something rises, it moves upwards.
Clouds of birds rose from the tree-tops.
When someone who is sitting rises, they stand up. You can also use rise to say that someone gets out of bed in the morning. See entry at rise - raise.
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