How to get a used car dealer to honor warranty for repairs required two weeks after purchase?

I bought a used car from an independent automobile dealership, mileage 59,000. The car was being sold "with warranty" not "as is". Two weeks later there was a defect in the exhaust system found by a mechanic (est. repair cost $1000). I know the defect existed on the car when I bought it and I think it's possible to prove it. Dealer is refusing to repair. Are dealers required to disclose defects to buyers? I asked about any problems with the car several times before I bought it. The auto dealer said there weren't any. I was also told that the car had inspection and 60,000 miles maintenance done (which included exhaust system check per manufacturer's recommendation). Does implied warranty apply in this case? I want the dealer to either repair the problem or cancel the contract. Is it realistic? What are my options? State: Delaware.

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