Here are some video resources showing complete examples (from Khan Academy). I hope they help!
-Prof. Reitz
Example 1 — in which the characteristic equation has two distinct real roots.
Example 2 — in which the characteristic equation has one repeated (real) root.
Example 3 — in which the characteristic equation has complex roots.
Posted in Resources
Tagged characteristic equation, constant coefficients, homogeneous, khan academy, second order, videos
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