Two different size tires on the rear?

Bought a truck the other day , tire blew out in the front. I had a spare on a 17 inch rim (rest is 15s) the tire on the 17 inch rim standing next to the 15 inch seems to be about 3 inches maybe 4 inches taller. Had to go down the road the other day and when I started to slow down the whole truck started shaking... show more Bought a truck the other day , tire blew out in the front. I had a spare on a 17 inch rim (rest is 15s) the tire on the 17 inch rim standing next to the 15 inch seems to be about 3 inches maybe 4 inches taller. Had to go down the road the other day and when I started to slow down the whole truck started shaking uncontrollably. Can that one tire cause the truck to shake like that? Happened a couple times and I had to slow the truck right down to 15-20 mph.
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