Skip to main content
Log in

Several classes of integrable nonlinear ordinary differential equations (I) first-order equations

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

In this paper we give some results of integrability and several classes of integrable equations of first-order nonlinear ordinary differential equations. Many known results of integrability and integrable equations are special cases of them. They may be applied in physics and mechanics, and to derive soliton equations and find soliton solutions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Li Hong-xiang, Elementary quadratures of ordinary differential equations,Amer. Math. Monthly,89, 3 (1982), 198–208;MR 83d: 34008.

    Google Scholar 

  2. Wang Cun-zheng, Formulas for solutions of differential equations, I. Formulas for solutions of higher-order linear and nonlinear ordinary differential equations with variable coefficients,Acta Math. Appl. Sinica,5, 3 (1982), 274–284;MR 84c: 34003. (in Chinese)

    Google Scholar 

  3. Li Hong-xiang, On periodic solutions of several classes of R Riccati's equation and second-order differential equations,Appl. Math. and Mech. (English Edition),3, 2 (1982), 225–232;MR 83m: 34036.

    Google Scholar 

  4. Li Hong-xiang, On the finding of solutions for several classes of higher-order linear differential equations with variable coefficients,Acta Math. Appl. Sinica,6, 1 (1983), 29–33:MR 85h: 34003. (in Chinese)

    Google Scholar 

  5. Wang Cun-zheng, Formulas for solutions of differential equations,Kexue Tongbao,30, 16 (1985), 1211–1214. (Chinese Ed.)

    Google Scholar 

  6. Wang Cun-zheng, Several nonlinear partial differential equations and their soliton solutions,Acta Mathematica Scientia,5, 1 (1985), 43–51. (in Chinese)

    Google Scholar 

  7. Kamke, E., Differentialgleichungen: Lösungsmethoden und Lösungen, I.Gewöhnliche Differentialgleichungen, 9 Aufl., B. G. Teubner Stuttgart (1977).

    Google Scholar 

  8. Murphy, G. M.,Ordinary Differential Equations and Their Solutions, D. Van Nostrand, New York (1960).

    Google Scholar 

  9. Zheng Long-xi, On several types of integrable first-order differential equations with variable coefficients,Higher Math.,2, 4 (1986), 158–162. (in Chinese)

    Google Scholar 

  10. Li Hong-xiang, Some supplements to Kamke's handbook “Gewöhnliche Differentialgleichungen”, I, II,J. Shanghai Inst. of Railway Tech.,7, 1 (1986), 9–22;7, 2 (1986), 27–38. (in Chinese).

    Google Scholar 

  11. Li Hong-xiang and Fan Xing, Re-discussion on elementary quadratures of ordinary differential equatins,J. Shanghai Inst. of Railway Tech.,8, 2 (1987), 1–15.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by Lou Shi-bo

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hong-xiang, L., Starc, Z.F. Several classes of integrable nonlinear ordinary differential equations (I) first-order equations. Appl Math Mech 11, 263–269 (1990). https://doi.org/10.1007/BF02015207

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02015207

Keywords

Navigation