First, your “sample” is not a compound sentence. It is a simple clause with sentence punctuation (capital letter and period). There is no reason to separate the subject from the predicate with a / (called a solidus). Secondly, the solidus’ function is ambiguous, according to the Chicago Manual of Style. It is mostly a visual device, not punctuation, and can take the place of a semicolon to emphasize a distinct parallel relationship between two clauses, thus:
Our moon is usually simply called “the moon”/ our sun is simply called “the sun.” But astronomers use more precise and exclusionary terms.
In a normal multi-clause sentence, the solidus should be avoided. Your problem sentence --"The boys went to the park, but they didn't do anything." -- would not benefit from an insertion of a solidus in place of the comma, because the "but" is a conjunction that serves a purpose, to show a negation between two clauses. A solidus in place of "but" would change the meaning of the sentence.
However, if you are using the solidus as part of a grammatical exercise in recognizing and indicating complete subject and predicate, then you would use the solidus quite simply, like this:
- The boys/went to the park, but they/didn't do anything.