Resolviendo ecuaciones diferenciales ordinarias con Symbolic Math Toolbox™ (Matlab) y SymPy (Python)


  • Gerardo Ortigoza Universidad Veracruzana
  • Roberto Iñaki Ponce de la Cruz Herrera Universidad Veracruzana



ordinary differential equations, symbolic solution, Matlab, Simpy Python


This paper shows solutions of ordinary differential equations (EDOS) obtained by using two symbolic packages: Symbolic Math Toolbox™ (Matlab) and SymPy (Python). The basic instructions to obtain solutions of both packages are explained step by step, through a group of examples from a traditional ordinary differential equations course. Differential equations that are solved with methods such as: separable variables, linear equations, indeterminate coefficients, variation of parameters, power series, Laplace transform, and numerical solutions are included. By means of the symbolic computation carried out with these packages it is possible to obtain the solution of linear systems, as well as the visualization of the direction field of a differential equation or of a non-linear system of differential equations. The main contribution of this work consists in providing the reader with a practical guide that allows him to start the study of differential equations assisted by Symbolic Math Toolbox™ or SymPy. Among the benefits of using these computational tools in teaching and/or learning practices, it is shown how the use of symbolic or numerical computation saves us effort in the computation of tedious calculations; focusing attention on important ideas and concepts such as: the relationship between the mathematical model and its physical counterpart, asymptotic behavior and qualitative analysis of the solutions.

Author Biography

Roberto Iñaki Ponce de la Cruz Herrera, Universidad Veracruzana

Investigador Tiempo Completo Instituto de Ingeniería UV


L. Kwan and M.A. Serdina, Impact of Using Graphing Calculator in Problem Solving, International Electronic Journal of Mathematics Education, (2018), 13(3).

F. Zeynivandnezhad, Z. Ismail Z. and Y.M. Yusof, Teaching mathematical structures in differential equations using a computer algebra system to engineering students, IEEE 7th International Conference on Engineering Education (ICEED), Kanazawa, Japan, 2015, pp. 10-15,

R. Gilbert, G. Hsiao, R. Ronkese, Maple Projects of Differential equations, 2nd Edition, Chapman and Hall /CRC, 2021

M. Abell, J. Braselton,Differential equations with Mathematica, 4th edition, 2016

M. Abrofarakh, T. Bux, Solving Ordinary Differential Equations with Matlab: Learning matlab in 2 hours, kindle edition, 2020

G. Lindfield, J. Penny, Numerical Methods using matlab, (4th edition kindle, 2019)

E. Lozada, C. Guerrero, A. Coronel, R. Medina, Classroom Methodologies for teaching and learning differential equations: A systematic literature review and biblioimetric analysis, Mathematics 9 (2021) 745

B.K. Amangeldievna, Formation of sustainable motivation to study the subject Differential Equations, Eurasian journal of learning and academic teaching, l7 (2022)

A. C. Brandi and R.E. García, Motivating engineering students to math classes: practical experience teaching ordinary differential equations, IEEE Frontiers in Education Conference 2017

C. Coelho, R. Marreiros and A. C. Conceicao, Interactive learning of modeling with ordinary differential equations, SYMCOMP, Portugal 2015

O. N. Kwon, Conceptualizing the realistic mathematics education approach in the teaching and learning of ordinary differential equations, International conference on the teaching of mathematics (at the undergrade level, 2002)

C. Guerrero, M. Camacho, and H.R. Mejía, Dificultades de los estudiantes en la interpretación de las soluciones de ecuaciones diferenciales ordinarias que modelan un problema, Enseñanza de la ciencia, 28 (2010) 341-352

O. N. Kwon, Differential Equations Teaching and Learning, Encyclopedia of Mathematics Education pp 220-223, Springer, 2020

S. Habre, Improving understanding in ordinary differential equations through writing in a dynamical environment, Teaching Mathematics and its Applications: An International Journal of the IMA, 31 (2012) 153

A. P. C. Lopes, and F. da Silva Reis, Contributions of mathematical modelling for learning differential equations in the remote teaching context Acta Scientiae, 24 (2022) 184

B.H. West, Teaching Differential Equations without Computer Graphics Solutions is a Crime, CODEE Journal 11 (2018)

G. Ortigoza, Resolviendo ecuaciones diferenciales ordinarias con Maple y Mathematica, Rev. Mex. Fis. E., 53 (2007) 155

G. Ortigoza, Ecuaciones diferenciales Ordinarias con Maxima, Rev. Edu. Mat., 21 (2009) 143

website Matlab help center symbolic toolbox solving odes,

Sympy 1.8 documentation, Sympy Modules Reference, ODE, disponible en

Matlab Live Editor, disponible en

The scientific Python development environment,

R. L. Lipsman, J. E. Osborn, and J. M. Rosenberg, The SCHOL Project at the University of Maryland: Using Mathematical Software in the Teaching of Sophomore Differential Equations, J. Num. Analysis, Industrial and Applied Mathematics, 3 (2008) 81

S. M. Maat, and E. Zakaria, Use of computer algebra systems in teaching and learning of ordinary differential equations among engineering technology students, In book: OutcomeBased Science, Technology, Engineering, and Mathematics Education, 2012

N. Lohgheswary, Z.M. Nopiah, E. Zakaria, A.A. Aziz and S. Salmaliza, Incorporating Computer Algebra System in Differential Equations Syllabus, Journal of Engineering and Applied Sciences, 14 (2019) 7475-7480

S. M. Maat, E. Zakaria, Exploring students’ understanding of ordinary differential equations using computer algebraic system (Cas), the Turkish journal of educational technology, 10 (2011) 13

F. Zeynivandnezhad, R. Bates, Explicating mathematical thinking in differential equations using a computer algebra system, International journal of mathematical education in science and technology, 2017

N. Eyrikh, R. Bazhenov, T. Gorbunova, N. Markova and A. Zhunusakunova, The Advantages of Using Computer Algebra System Maple in Learning Differential Equation, V International Conference on Information Technologies in Engineering Education (Inforino), (2020) 1-5,

B.I. Zaleha, F. Zeynivandnezhad, B.M.Y. Yudariah, S. Bambang,Integrating a computer algebra system as the pedagogical tool for enhancing mathematical thinking in learning differential equations, Proceedings of the IETEC’13 Conference, Ho Chi Minh City, Vietnam, 2013

B. F. Azevedo, A.I. Pereira, F. P. Fernandes, M. F. Pacheco, Mathematics learning and assessment using MathE platform: A case study, Educational and Information Technologies 27 (2022) 1747-1769

I. Drori et al., A neural network solves, explains, and generates university math problems by program synthesis and few-shot learning at human level, Proc Natl Acad Sci U S A. 119 (2022) e2123433119

M. Kanda, Ordinary Differential equations and physical phenomena a short introduction with Python, Asakura Publishing, 2020

S. Chapra and D. Clough, Applied Numerical Methods with Python for engineers and scientists, 1st Ed, McGraw Hill, 2021

R. Johansson, Numerical Python: Scientific Computing and Data Science Applications with Numpy, SciPy and Matplotlib, second edition Apress, 2019

S. Linge, H. P. Langtangen, Programming for Computations Python: A Gentle Introduction to Numerical Simulations with Python 3.6, Second Edition, springer Open, 2018.E 20




How to Cite

G. Ortigoza and R. I. Ponce de la Cruz Herrera, “Resolviendo ecuaciones diferenciales ordinarias con Symbolic Math Toolbox™ (Matlab) y SymPy (Python)”, Rev. Mex. Fis. E, vol. 20, no. 2 Jul-Dec, pp. 020209 1–, Jun. 2023.