1. E. A. Coddington and N. Levinson, Theory of Ordinary
Differential Equations, McGraw–Hill, New York, 1955.#
2. E. L. Ince, Ordinary Differential Equations, Dover Pub
lications, New York, 1956.#
3. NISTDigital Library of Mathematical Functions, “Airy,
Bessel, Legendre, and Parabolic-Cylinder Functions,”
National Institute of Standards and Technology, avail
able at https://dlmf.nist.gov.#
4. M. Abramowitz and I. A. Stegun, Handbook of Mathe
matical Functions with Formulas, Graphs, and Mathe
matical Tables, National Bureau of Standards, 1964.#
5. M. J. Fogaça and E. L. Cardoso, “A Systematic Ap
proach to Obtain the Analytical Solution for Linear
Second Order Ordinary Differential Equations: Part I,”
Journal of the Brazilian Society of Mechanical Sci
ences and Engineering, 2024, DOI: 10.1007/s40430
024-04755-8.#
6. P. Zheng, J. Luo, S. Li and X. Dong, “Elastic Transfor
mation Method for Solving Ordinary Differential Equa
tions with Variable Coefficients,” AIMS Mathematics
7(1) (2022), 1307–1320, DOI: 10.3934/math.2022077.#
7. M. A. Jama, K. Giterere and D. G. Kioi, “A Novel
Analytic Method with Integral Transform for Solving
Classes of Second and Third Order Ordinary Linear
Differential Equations with Variable Coefficients,” Ap
plied and Computational Mathematics 14(2) (2025),
78–89, DOI: 10.11648/j.acm.20251402.11."
8. M. Gadella and L. P. Lara, “A Note on Lin
ear Differential Equations with Variable Coeffi
cients,” arXiv preprint, arXiv:2410.08630 (2024), DOI:
10.48550/arXiv.2410.08630.#
9. E. Capelas de Oliveira and J. E. Maiorino, “Ordinary
Differential Equations,” in Analytical Methods in Ap
plied Mathematics, Springer Nature, 2025.#
10. J. Lebl, “Higher Order Linear ODEs,” Mathematics Li
breTexts, updated 2025, https://math.libretexts.org."
11. SciPy Developers, “scipy.integrate.solve_ivp
Documentation,”
SciPy
API
https://docs.scipy.org, accessed 2026.
Reference,#
12. E. Hairer, S. P. Nørsett and G. Wanner, Solving Ordi
nary Differential Equations I: Nonstiff Problems, 2nd
ed., Springer, 1993.#
