Wong, James S. W. On rectifiable oscillation of Euler type second order linear differential equations. (English) Zbl 1182.34049 Electron. J. Qual. Theory Differ. Equ. 2007, Paper No. 20, 12 p. (2007). Summary: We study the oscillatory behavior of solutions of the second order linear differential equation of Euler type: \[ y'' + \lambda x^{-\alpha} y = 0, \;x \in (0, 1],\tag{E} \]where \(\lambda > 0\) and \(\alpha> 2\). Theorem (a) For \(2 \leq \alpha < 4\), all solution curves of \((E)\) have finite arc length; (b) For \(\alpha \geq 4\), all solution curves of \((E)\) have infinite arc length. This answers an open problem posed by M. Pasic. Cited in 8 Documents MSC: 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34A30 Linear ordinary differential equations and systems PDFBibTeX XMLCite \textit{J. S. W. Wong}, Electron. J. Qual. Theory Differ. Equ. 2007, Paper No. 20, 12 p. (2007; Zbl 1182.34049) Full Text: DOI EuDML EMIS