Which of the following is a non-narcotic anti-tussive medication?

Dextromethorphan is indeed classified as a non-narcotic anti-tussive medication. It works by suppressing the cough reflex in the brain, specifically in the medullary cough center. Unlike narcotic cough suppressants, such as codeine phosphate and hydrocodone, dextromethorphan does not have significant analgesic properties and is not considered addictive, making it suitable for over-the-counter use.

This property makes it particularly advantageous for treating coughs without the side effects often associated with narcotics, such as drowsiness and the potential for dependence. As a widely used ingredient in cough syrups and cold medications, dextromethorphan provides relief from coughing without the risks associated with narcotic medications.

In contrast, codeine phosphate and hydrocodone are both opioid medications that serve as effective cough suppressants but carry risks such as dependence and respiratory depression. Prednisolone, a corticosteroid, does not function as a cough suppressant but rather reduces inflammation in conditions like asthma or allergies. Thus, dextromethorphan stands out as the correct choice for a non-narcotic anti-tussive.