# Asymptotic analysis of an algebraic equation

1. Oct 20, 2012

### AlonsoMcLaren

1. The problem statement, all variables and given/known data

Perform an analysis of the algebraic equation y=exp(xy) near x=1/e by substituting y=e+d(x), where d→0 as x→1/e. Solve approximately for d(x) to show that near x=1/e, y(x) has a square root singularity.
2. Relevant equations

I don't think there are "relevant equations"

3. The attempt at a solution

ln y = xy
as x-> 1/e, ln (e+d) ~ ln e , that is, ln y ~ 1
1~x(e+d)
d~(1/x)-e
y=e+d
y~1/x
So where is "square root singularity"?