Substitution methods for the automatic symbolic solution of differential equations of first order and first degree

  • Peter Schmidt
5. Differential Equations
Part of the Lecture Notes in Computer Science book series (LNCS, volume 72)


Some heuristics that suggest substitutions for solving differential equations of first order and first degree are presented. The test results with these heuristics show that ‘satisfying’ heuristics can be developed for this type of differential equations. Moreover, test results show that a program utilizing the basic elementary solution methods and a comparatively small set of such heuristics is able to solve most of the elementarily solvable differential equations of first order and first degree, which are collected in the textbooks of Kamke and Murphy.


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  1. Kamke, E. (1961): "Differentialgleichungen — Lösungsmethoden und Lösungen, 1. Gewöhnliche Differentialgleichungen", Akad. Verl. Ges. Geest&Portig K.G., Leipzig, 7th edition.Google Scholar
  2. Moses, J. (1967): "Symbolic Integration", Report MAC TR-47, Project MAC, MIT, Cambr., Mass., Dec 1967.Google Scholar
  3. Murphy, G.M. (1960): "Ordinary Differential Equations", D. van Nostrand Comp., Inc., Princeton, New Jersey.Google Scholar
  4. ODER (1976): Listing of the program ODER, MIT, Aug. 1976.Google Scholar
  5. Schmidt, P. (1976): "Automatic Symbolic Solution of Differential Equations of First Order and First Degree", 1976 ACM Symposium on Symbolic and Algebraic Computation, Yorktown Heights, N.Y., Aug. 1976, pp. 114–125.Google Scholar
  6. Schmidt, P. (1977): "Maschinelle symbolische Lösung von Differentialgleichungen 1. Ordnung und 1. Grades", Informatik Berichte der Universität Bonn, Nr. 17, Nov. 1977.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Peter Schmidt
    • 1
  1. 1.Institut für InformatikUniversität BonnBonnWest Germany

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