Capital or small letter in science text [closed]

It depends on the context. If you've defined the equations explicitly as Equation 1, Equation 2, and Equation 3, you should keep them capitalized. If you've defined them with some other name, then don't capitalize them.

My field is computer science, and it is exceedingly common to refer to things as Figure 1, or Lemma 2, or Integer i. You are naming them and thus they are proper nouns and should be capitalized. For example, consider

https://homes.cs.washington.edu/~lazowska/qsp/Images/Chap_01.pdf

Apologies in advance, it just happened to be something I had open at this very moment. In this case, you can see images captioned Figure X and then later referred to as proper nouns in the text. Just do a text search for "Figure" and you'll see.

If, however, those equations were introduced as something like Boyle's Law, Stokes Theorem, and The Second Law of Thermodynamics, and this is the first time you're describing them as equations 1, 2, 3 (presumably because they appear in that order), do not capitalize equations.