While working as an editor and reading in my leisure time, I've seen numerous authors mistakenly use "divulge" instead of "delve." These words do not have the same meaning and are not interchangeable.
Delve
To delve is to research or make painstaking inquiries into something. Delve is often used when referencing digging into information, such as a therapist requesting a client delve into their past in an attempt to determine the root cause of certain behaviors. It is the act within itself of looking into something.
Divulge
To divulge, on the other hand, is to make private or sensitive information known. Divulge is commonly used when referencing a person's secrets, medical information, or any other personal or private information that the general public should not be made aware of or have access to. Divulge is the act of revealing, releasing, or providing information.
While these terms both involve the exploration of information on some level, they are not interchangeable. They have distinct meanings and uses, and one should not be used in the place of the other.