Engineering Mathematics, Volume II, Second Edition

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4.29 The Cauchy-Euler Homogeneous Linear Equation

Consider the following differential equation with variable coefficients:

where a_i are constant and F is a function of x. This equation is known as Cauchy-Euler homogeneous linear equation (orequidimensional equation). The Cauchy-Euler homogeneous linear equation can be reduced to linear differential equation with constant coefficients by putting x =e^t or t = log x. Then

Now

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