>>12865514So you need to be able to differentiate twice, and that needs to be homogeneous. If it isn't, something else is going on that's left out of your function.
https://math.mit.edu/~jorloff/18.04/notes/topic5.pdfThe solution to the DE is going to be based in e, as simple as it gets. e to an imaginary number includes sine and cosine.
Let's say you are looking at a point of internal stress, and it's at 100 kips. Is that 100 kips on quicksand, or a pressure cooker?
I think of alternating current. You want 110 volts at from 109 to 110, not from 110 to 109, to get the full power. The imaginary part reflects where you are at.
I also think of picking apples in an orchard. The imaginary part is like the blossoms. You don't get any extra apples, but the orchard will grow back if you count the blossoms.
