Which of the following is more correct?

"we show our results on the example of the Duffing equation"


"we show our results using the Duffing equation as an example"

I am very thankful for any help.


The first sentence is arguably incorrect: the verb "show" does not usuallt take "on" as a preposition. This sentence may be understood, but it's not eloquent writing.

The second sentence is correct and eloquent.

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