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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a Cauchy Euler equation (also known as the Euler Cauchy equation, or simply Euler''s equation) is a linear homogeneous ordinary differential equation with variable coefficients. It is sometimes referred to as an equidimensional equation. Because of its simple structure the equation can be replaced with an equivalent equation with constant coefficients which can then be solved explicitly.