Are these 2 equations some of general formulas of infinitesimal length?
This is an example how practical engineers and also many physicists think math. Continuously distributed material is divided to infinitely small elements and a differential equation is written by assuming those infinitely small elements obey circuit laws. Many in practice useful laws are found by thinking like this, for ex. the famous telegrapher's equations for transmission lines.
The principle to divide areas to infinitely small elements became mainstream in 1700's. Electronics did not exist then but the idea was used in mechanics.
That principle contains logic caveats which lead easily to fatal errors, but fortunately there are also persons called mathematicians who can do the job in a rigorous way and kick the practical men back to the road if needed.
The caveats lurk where the equations allow more complex functions that humans are able to think. Only rigorous logical reasoning can keep wrong assumptions out. Guys like Gauss and Cauchy started in 1800's to put things into the shape. They didn't make worthless the work of the pioneers who with no sorrow calculated with infinitely small quantities. That's because so many things found by pioneers are still used in everyday engineering and mathematicians have checked their foundations.