I assume this is attached to an outdoor spigot. If so, the water is entering the hose faster than it exits. Instead of turning the faucet full on, reduce the pressure by turning on only 1/4 or half way.

Thanks for responding. The hose is used with a hand-held sprayer that has an adjustable nozzle. Sometimes the hose would separate from the tap end, and sometimes from the spray-nozzle end. A few days ago I found a shop that sells drip irrigation systems for home gardens. They sell clip-on tap connectors for HDPE irrigation pipes. These connectors require pipes be attached to them using old-fashioned hose clamps. I attached two half-inch connectors to my garden hose using the clamps supplied, and since then have had no hose-burst problems.