The discussion focuses on converting a Sturm-Liouville problem, specifically the equation xy" + 2y' + λxy = 0 with boundary conditions y(∏) = 2 and y(2∏) = 0, into Bessel's equation. Daniel, the original poster, seeks guidance on solving this problem. A suggested approach involves using a series solution, particularly noting that x=0 is a regular singular point, and considering substitutions such as u=yx to simplify the equation.
PREREQUISITESMathematicians, physicists, and engineering students dealing with differential equations, particularly those interested in Sturm-Liouville problems and their applications to Bessel functions.
fantastic_dan said:Hello, I've been given a Sturm Liouville problem to solve:
xy" + 2y' + λxy = 0
y(∏) = 2, y(2∏) = 0
I'm not sure how to solve this problem. However, it looks similar to Bessel's equation. Any ideas?
Thanks,
Daniel
LCKurtz said:I would suggest trying a series solution noting ##x=0## is a regular singular point.