What is the name of your state (only U.S. law)?
What is the name of your state or, if not in the US, what is the name of your country?
Generally when you purchase a car from a private seller, the car is purchased "as is." It is up to the buyer to inspect the car prior to purchase so that if there are any defects, they are discovered at that time. If an inspection is not done, and the car has defects not disclosed by the seller (or unknown to the seller), the purchaser usually has little legal recourse.