The second‐order homogeneous Cauchy‐Euler equidimensional equation has the form. where a, b, and c are constants (and a ≠ 0). The quickest way to solve this linear equation is to is to substitute y = x m and solve for m. If y = x m , then. so

Get StartedA second-order differential equation is called anEuler equation if it can be written as αx2y′′ + βxy′ + γy = 0 where α, β and γ are constants (in fact, we will assume they are real-valued constants).

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A more general form of an Euler Equation is, \[a{\left( {x - {x_0}} \right)^2}y'' + b\left( {x - {x_0}} \right)y' + cy = 0\] and we can ask for solutions in any interval not containing

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