The firstthing I need to note is this is for a HISTORY of math course, so we have to use non modern techniques in most cases, some not. In other words, thequestion describes how to solve them. I'm also on a compyuter with a terrible keyboard so I'm doing my best.
Derive the power series for the logarithm by beginning with dy=1/(x+1)dx and assuming that y is apowerseries in x with undetermined coeeficients, and solving simple equations to determine each coeefficient in turn.
2)solve the fluxonial equation x*/y*=2/x+3-x^2 by replacing x with x+1 and then using power series techniques
NOTE: x* and y* are simply x with a dot above it, indicting derivtive of x in the old notation
The Attempt at a Solution
1) Well I know that if i intergate this i get the corretc solution, but they didnt have our modern integrating notations at the time. (this is Leibniz) and it syas to determine coofeicients, so I have no idea where to start
2) i had no idea what to do here. I repce x with x+1 and got 2/(x+1) (whihc is 2 times the same expandion in 1) ) +3-(x^2+2x+1)
No idea wht to do after that, I don't even know what I'm suposed to solve for.