Methods of solving systems of ordinary linear differential equations: A comparative analysis

Date of Publication


Document Type


Degree Name

Doctor of Philosophy in Science Education Major in Mathematics

Subject Categories

Ordinary Differential Equations and Applied Dynamics


Br. Andrew Gonzalez FSC College of Education


Science Education


This is a comparative analysis of the Rootselaar's Method (R-Method) and Eigenvalue-Eigenvector Method (E-E Method) in solving the systems of ordinary linear differential equations (SOLDE).Prior to the comparison, tests in both Algebra and Trigonometry were developed and validated. The results of the validated tests served as the bases of grouping the respondents - either to the R-method or the E-E method. Thus, this research underwent two major parts. These were (1) the development and validation of the two tests and (2) the experimental method of solving SOLDE.One hundred eighty items were constructed for each of the Algebra and Trigonometry subjects. These were printed in three forms (A,B,C) which contained 60 items each. All the three forms for both Algebra and Trigonometry were administered to 150 College of Engineering freshmen of Mariano Marcos State University (MMSU). They were enrolled for the first semester of school year 1994-1995. The tests were subjected to item analysis. Sixty choice items from each were considered to comprise the final form of the tests.The final form of the tests were again administered to 148 freshman engineering students of Pangasinan University (PSU) during the second semester of SY 1994-95. This was done for revalidation purposes.

The respondents were intact classes of third year engineering students of Advanced Engineering Mathematics from MMSU and PSU. In PSU, the experimental group was composed of 38 Civil Engineering (CE) students while the control group was composed of 18 Electrical Engineering (EE) students. In MMSU, 15 EE students made up the experimental group while 15 CE students consisted the control group. The non-equivalence pretest-posttest design was used.Before starting the experiment which lasted for 8 weeks, all respondents were given standardized tests in Algebra and Trigonometry. The respondents' scores were averaged and grouped accordingly to either high or low. Four groups were formed - experimental-high, experimental-low, control-high, and control-low. The researcher handled both the experimental and control groups. In solving SOLDE, the respondents in the experimental group were taught using method II (E-E method).The data were subjected to ANCOVA, the weighted average grade in Differential, and Integral Calculus and Differential Equations as covariates. The students taught under R-method scored significantly higher than those exposed to E-E method. This was true to both high and low groups.The high-ability group scored significantly higher than the low-ability group after exposure to the methods of solving SOLDE.The R-method, under particular cases, significantly enhanced the performance of the students in solving SOLDE. None of the methods was significantly more compatible with a particular group in terms of solving SOLDE.

Abstract Format






Accession Number


Shelf Location

Archives, The Learning Commons, 12F Henry Sy Sr. Hall

Physical Description

217 numb. leaves ; Computer print-out


Differential equations, Linear; Problem solving; Mathematics--Problems, exercises, etc.; Algebra; Educational tests and measurements--Validity; Engineering students; Mariano Marcos State University--Students

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