What is the best way to teach the solution of second-order equations for middle stage students?

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Mohamed Abdallah Turky

http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_FREE_DIFFEQ_I.PDF
http://archives.math.utk.edu/ICTCM/VOL08/C059/paper.pdf

Mariappan Jawaharlal

Not sure the reasoning behind teaching at middle school level. If you have to do that (in some ways, this is similar to teaching calculus very early), I will start with specific examples that lead to the introduction of the subject. I will stay away from traditional textbooks which can overwhelm even college students. Focus on linears systems with constant coefficients.

Teresa M. Vidal-Valdivia

You can use Strategies of Heuristic Polya, in four steps