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Inspiring and engaging high school students with science and technology education in regional Australia
Unification of the common methods for solving the firstorder linear ordinary differential equations
1.  School of Engineering and Technology, Central Queensland University, Bruce Highway, North Rockhampton, QLD 4702, Australia 
A good understanding of the mathematical processes of solving the firstorder linear ordinary differential equations (ODEs) is the foundation for undergraduate students in science and engineering programs to progress smoothly to advanced ODEs and/or partial differential equations (PDEs) later. However, different methods for solving the firstorder linear ODEs are presented in various textbooks and resources, which often confuses students in their choice of the method for solving the ODEs. This special tutorial note presents the practices the author used to address such confusions in solving the firstorder linear ODEs for students engaged in the bachelorette engineering studies at a regional university in Australia in recent years. The derivation processes of the four commonly adopted methods for solving the firstorder linear ODEs, including three explicit methods and one implicit method presented in many textbooks, are presented first, followed by the logical interconnections that unify these four methods to clarify student's confusions on different presentations of the procedures and the solutions in different sources. Comparisons among these methods are also made.
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References:
[1] 
Iasson Karafyllis, Lars Grüne. Feedback stabilization methods for the numerical solution of ordinary differential equations. Discrete and Continuous Dynamical Systems  B, 2011, 16 (1) : 283317. doi: 10.3934/dcdsb.2011.16.283 
[2] 
Bernard Dacorogna, Alessandro Ferriero. Regularity and selecting principles for implicit ordinary differential equations. Discrete and Continuous Dynamical Systems  B, 2009, 11 (1) : 87101. doi: 10.3934/dcdsb.2009.11.87 
[3] 
Roberto Garrappa, Eleonora Messina, Antonia Vecchio. Effect of perturbation in the numerical solution of fractional differential equations. Discrete and Continuous Dynamical Systems  B, 2018, 23 (7) : 26792694. doi: 10.3934/dcdsb.2017188 
[4] 
V.N. Malozemov, A.V. Omelchenko. On a discrete optimal control problem with an explicit solution. Journal of Industrial and Management Optimization, 2006, 2 (1) : 5562. doi: 10.3934/jimo.2006.2.55 
[5] 
Nguyen Thi Hoai. Asymptotic approximation to a solution of a singularly perturbed linearquadratic optimal control problem with secondorder linear ordinary differential equation of state variable. Numerical Algebra, Control and Optimization, 2021, 11 (4) : 495512. doi: 10.3934/naco.2020040 
[6] 
David W. Pravica, Michael J. Spurr. Unique summing of formal power series solutions to advanced and delayed differential equations. Conference Publications, 2005, 2005 (Special) : 730737. doi: 10.3934/proc.2005.2005.730 
[7] 
Burcu Gürbüz. A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021069 
[8] 
Minoo Kamrani. Numerical solution of partial differential equations with stochastic Neumann boundary conditions. Discrete and Continuous Dynamical Systems  B, 2019, 24 (10) : 53375354. doi: 10.3934/dcdsb.2019061 
[9] 
Sertan Alkan. A new solution method for nonlinear fractional integrodifferential equations. Discrete and Continuous Dynamical Systems  S, 2015, 8 (6) : 10651077. doi: 10.3934/dcdss.2015.8.1065 
[10] 
Changrong Zhu, Bin Long. The periodic solutions bifurcated from a homoclinic solution for parabolic differential equations. Discrete and Continuous Dynamical Systems  B, 2016, 21 (10) : 37933808. doi: 10.3934/dcdsb.2016121 
[11] 
Huanting Li, Yunfei Peng, Kuilin Wu. The existence and properties of the solution of a class of nonlinear differential equations with switching at variable times. Discrete and Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021289 
[12] 
Bara Kim, Jeongsim Kim. Explicit solution for the stationary distribution of a discretetime finite buffer queue. Journal of Industrial and Management Optimization, 2016, 12 (3) : 11211133. doi: 10.3934/jimo.2016.12.1121 
[13] 
Oana Pocovnicu. Explicit formula for the solution of the Szegö equation on the real line and applications. Discrete and Continuous Dynamical Systems, 2011, 31 (3) : 607649. doi: 10.3934/dcds.2011.31.607 
[14] 
Zvi Artstein. Averaging of ordinary differential equations with slowly varying averages. Discrete and Continuous Dynamical Systems  B, 2010, 14 (2) : 353365. doi: 10.3934/dcdsb.2010.14.353 
[15] 
Farid Tari. Twoparameter families of implicit differential equations. Discrete and Continuous Dynamical Systems, 2005, 13 (1) : 139162. doi: 10.3934/dcds.2005.13.139 
[16] 
Josef Diblík, Klara Janglajew, Mária Kúdelčíková. An explicit coefficient criterion for the existence of positive solutions to the linear advanced equation. Discrete and Continuous Dynamical Systems  B, 2014, 19 (8) : 24612467. doi: 10.3934/dcdsb.2014.19.2461 
[17] 
Jian Su, Yinnian He. The almost unconditional convergence of the Euler implicit/explicit scheme for the three dimensional nonstationary NavierStokes equations. Discrete and Continuous Dynamical Systems  B, 2017, 22 (9) : 34213438. doi: 10.3934/dcdsb.2017173 
[18] 
A. Domoshnitsky. About maximum principles for one of the components of solution vector and stability for systems of linear delay differential equations. Conference Publications, 2011, 2011 (Special) : 373380. doi: 10.3934/proc.2011.2011.373 
[19] 
Hermann Brunner. The numerical solution of weakly singular Volterra functional integrodifferential equations with variable delays. Communications on Pure and Applied Analysis, 2006, 5 (2) : 261276. doi: 10.3934/cpaa.2006.5.261 
[20] 
Thabet Abdeljawad, Mohammad Esmael Samei. Applying quantum calculus for the existence of solution of $ q $integrodifferential equations with three criteria. Discrete and Continuous Dynamical Systems  S, 2021, 14 (10) : 33513386. doi: 10.3934/dcdss.2020440 
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