- #1

roadrunner

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## Homework Statement

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.

1)

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

## Homework Equations

1) 1/(x+1)=1-x+x^2-x^3+....

## 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.

Thanks