All Title Author
Keywords Abstract

On Series Solutions of y''- f(x)y=0 and Applications

DOI: 10.1186/1687-1847-2013-47

Full-Text   Cite this paper   Add to My Lib


In this paper, we develop explicit expressions for the Taylor series coefficients in the formal Taylor series solution of the second order linear differential equation $y'' -f(x)y = 0$ for a given arbitrary function $f(x)$ in terms of initial conditions. As applications we apply our results to $f(x) = e^x, \cos(x)$ and Airy's equation, and give explicit formulas for the Taylor coefficients of $\exp(\sum_{k=0}^\infty a_{k}x^k)$ which is a long standing question.


comments powered by Disqus