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2nd order ODE with constant coeffcients: non-standard method of solution

Free ebook http://tinyurl.com/EngMathYTI present a direct and non-standard method of solution to the 2nd order homogeneous ODE with constant coefficients, namely$$y'' - 4y' + 4y = 0.$$I do not explicitly use the characteristic equation, rather I reduce the problem to the analysis of a first order ODE. Such a method shows exactly why the solution features exponential functions and illustrates where they come from,
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