HomePhilippine Journal of Material Science and Nanotechnologyvol. 8 no. 1 (2022)

Exact solutions of oscillator-inspired differential equations

Emmanuel T. Rodulfo

 

Abstract:

Exact solutions to certain homogeneous 2nd-order differential equations are presented by exploiting their links with the classical oscillator differential equation. The veracity of the exact solutions may be confirmed by the standard Fröbenius series solution, which we carry out for the Embden-Fowler differential equation.



References:

  1. H. D. Young, R. A. Freedman, A. L. Ford, & F. W. Sears, (2004). Sears and Zemansky's University Physics: with Modern Physics. San Francisco: Pearson Addison Wesley.
  2. H. Goldstein, (1951). Classical Mechanics (1st ed.). Addison-Wesley. ASIN B000OL8LOM.
  3. H. Goldstein, (1980). Classical Mechanics (2nd ed.). Addison-Wesley. ISBN 978-0-201-02918-5.
  4. H. Goldstein, C. P. Poole, J. L. Safko, (2001). Classical Mechanics (3rd ed.). Addison Wesley. ISBN 978-0-201-65702-9.
  5. G. Arfken and H. Weber (6 th Edition), Mathematical Methods for Physicists, Elsevier Academic Press.
  6. G. Arfken, Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, 1985.
  7. J. Janus and J. Myjak, “A generalized Embden-Fowler equation with a negative exponent,” Nonlinear Analysis, Theory, Methods & Applications, vol. 23, No. 8, p. 953-970, 1994.