In the Wikipedia article Diophantine set there is a section entitled "Further applications" in regards to Matiyasevich's theorem and it states:

Matiyasevich's theorem has since been used to prove that many problems from calculus and differential equations are unsolvable.

One can also derive the following stronger form of Gödel's first incompleteness theorem from Matiyasevich's result:

and then states the theorem. However, this section contains no specific citations. Could somebody provide me with references of this proof worthy of citation? Specifically, I mean the proof regarding the first incompleteness theorem. Granted, it is easy to see how Matiyasevich's theorem can prove Gödel's first incompleteness theorem, but I am looking for (possible the first) published paper with this result to be able to reference it.

Ch.VIandVIIor Herbert Enderton, Computability Theory: An Introduction to Recursion Theory, Academic Press (2011), page 119. And see Raymond Smullyan, Gödel's incompleteness theorems, Oxford (1992), apge 5. 2/2 $\endgroup$