The analytical and approximate solutions of ϵy″ = yy′
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Abstract The analytical and approximate soluions of ϵy ″ = yy ′ are developed and compared, and the analytical solution is evaluated numerically. The analytical soluion has several interesting properties: (i) it possesses three different types of solutions, constant, exponential, and tangent; (ii) for a two-point boundary value problem it has an undecidability aspect relative to which solution type holds; (iii) for the tangent solution type an infinite number of solutions exist, both continuous and discontinuous; (iv) even with the analytical solution known, its numerical evaluation can still be difficult to generate.
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