Exploring Students’ Difficulties in Solving Nonhomogeneous 2nd Order Ordinary Differential Equations with Initial Value Problems

Yunika Lestaria Ningsih, Anggria Septiani Mulbasari


This research aims to explore students’ difficulties in resolving Nonhomogeneous 2nd Order Ordinary Differential Equations with initial value problems. The method that can be used to solve this equation is the undetermined coefficient and the Laplace transformation. This research is used descriptive method. The subjects of this study were 73 students in the second year of the Mathematics Education. Data is collected through tests and interviews. Data were analyzed descriptive qualitative. The results of data analysis show that in undetermined coefficient method, students difficult in determining the particular solution of non-homogeneous second-order ordinary differential equations. This is due to student errors in the first step especially in determining the characteristics equation. Whereas, for the Laplace transformation method, students most difficulties are in the step of solving the subsidiary equation. This is due to the weakness of students in completing arithmetic operations in the form of fractions and partial fractions.



Ordinary differential equations; undetermined coefficient method; Laplace transformation.

Full Text:



Apriandi, D., & Krisdiana, I. (2016). Analisis Kesulitan Mahasiswa dalam Memahami Materi Integral Lipat Dua Pada Koordinat Polar Mata Kuliah Kalkulus Lanjut. Al-Jabar: Jurnal Pendidikan Matematika, 7(2), 123-134.

Boyce, W. E., & DiPrima, R. C. (2001). Elementary Differential Equations and Boundary Value Problems. New York: John Willey & Sons.

Budiyono, & Guspriati, W. (2009). Jenis-jenis Kesalahan dalam Menyelesaikan Soal Persamaan Diferensial Biasa (PDB) Studi Kasus pada Mahasiswa Semester V Program Studi Pendidikan Matematika Universitas Muhammadiyah Purworejo. Seminar Matematika dan Pendidikan Matematika FMIPA UNY (hal. 131-140). Yogyakarta: UNY.

Holmberg, M., & Bernhard, J. (2008). University teachers perspectives about difficulties for engineering students to understand the Laplace transform. Retrieved from https://pdfs.semanticscholar.org/f10a/ab80a1a04a968d4e2b7ecb8efa8f9f37566b.pdf:

Khotimah, & Masduki, R. P. (2016). Improving teaching quality and problem solving ability through contextual teaching and learning in differential equations: a lesson study approach. Journal of Research and Advances in Mathematics Education, 1(1), 1-13.

Kreyszig, E., Kreyszig, H., & Norminton, E. J. (2011). Advanced Engineering Mathematics. USA: John Wiley & Sons. Inc.

Kusuma, H., & Masduki. (2016). How students solve the logarithm? conceptual and prosedural uderstanding. Journal of Research and Advances in Mathematics Education, 1(1), 56-68.

Machin, M. C., Diaz, J. P., & Trigo, M. S. (2012). An exploration of students' conceptual knowledge built in a first ordinary differential equations course (part 1). The Teaching of Mathematics, XV, 1-20.

Macromah, U., Purnomo, M. E., Febriyanti, K., & Rahmawati, H. A. (2017). Arithmatics skill: Kesulitan Utama Mahasiswa dalam Menyelesaikan Soal Kalkulus Integral. Seminar Matematika dan Pendidikan Matematika UNY (hal. 365-372). Yogyakarta: UNY.

Naisunis, Y. P., Taneo, P. N., & Daniel, F. (2018). Analisis kesulitan mahasiswa dalam pemecahan masalah pada mata kuliah persamaan diferensial. Edumatica, 8(2), 107-119.

Ningsih, Y. L., & Rohana. (2018). Pemahaman Mahasiswa Terhadap Persamaan Diferensial Biasa Berdasarkan Teori APOS. JPPM, 11(1), 168-176.

Orton, A. (1983). Students' Understanding of Differentiation. Educational Studies in Mathematics, 235-250.

Prawoto, B., Hartono, S., & Fardah, D. (2018). Prospective teachers' difficulties in second order linier differential equation:a case of constructing methods in solving a non-homogeneous problem. IOP Conf.Series 1108, 012002, 1-5.

Rahmawati, A. (2017). Analisis Kesalahan Mahasiswa Pendidikan Matematika Dalam Menyelesaikan Soal Pertidaksamaan Pada Mata Kuliah Kalkulus I. Al-Jabar: Jurnal Pendidikan Matematika, 8(1), 81-90.

Rasmussen, C. (2001). New directions in differential equations. A framework for interpreting students' understandings and difficulties. The Journal of Mathematical Behavior, 20(1), 55-87.

Sugiyono. (2008). Metode Penelitian Pendidikan. Bandung: Alfabeta.

Vajravelu, K. (2018). Innovative strategies for learning and teaching of large differential classes. IEJME (International Electronic Journal of Mathematics Education), 13(2), 91-95.

DOI: http://dx.doi.org/10.24042/ajpm.v10i2.3726


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.


Creative Commons License
Al-Jabar : Jurnal Pendidikan Matematika is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.