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The only way to make a dog throw at home is to give hydrogen peroxide. This can be very irritating to the stomach and esophagus however. You can give him 3-5 table spoons orally and if he does not vomit within 20 minutes repeat it once.
The best way to make a dog vomit is with a medication called apomorphine which all emergency veterinarians have. It comes as an injection or as tablet that is put in the conjunctiva that a works better than peroxide. Once he has been made to vomit, the vet will give him activated charcoal to absorb anything that has left hi stomach or not come up with the vomit. I recommend taking Mickey to the vet even if he vomits at home so that he can be given activated charcoal and ideally he should be put on IV fluids and have his kidney values monitored for 24-48 hours. Both raisins and NSAIDs can cause acute kidney injury, so I would worry about him going in to acute renal failure even if he does vomit based on the dose and that he ate 2 potentially renal toxic substances.
If you are unable to hospitalize him, then your vet can discuss alternatives such as fluids under the skin at home (less ideal but will still help to flush out his system and may protect his kidneys) and returning for recheck blood work 24 and 48 hours post exposure. If at 48 hours his creatinine is normal (one of the things the kidney filters that tells how well it is working) or has not increased by 50% or more even if it remains in the normal range then he will likely be fine.