As for C ++, there will be no problem using a single header file and splitting the actual function implementations between the two files. However, if you need functions from "Second.cpp" in "First.cpp", you might want to see what happens in each of them, and maybe the functionality should be split into another file.
As a personal preference, I say that you should stick with one cpp file for each header file. Splitting the implementation will simply cause headaches later if you need to re-execute the implementation again.
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