Generating some linear second-order differential equations with undetermined coefficients by Linearly combining Frobenius and Legendre differential equations
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Legendre equation, Frobenius equation, Bessel equation, Series method, Frobenius method, Second-order linear differential equations with undetermined coefficients.
Abstract
This paper aims to generate some linear, second-order and homogeneous ordinary differential equations (ODEs) with variable and undetermined coefficients by linearly combining some well-known ODEs in mathematical physics community which are the Legendre and Frobenius (or Bessel as a special case) ODEs. Comparing the form of the generated ODEs with the original (mother) ODEs should allow us to facilitate choosing the appropriate method to solve such ODEs.....
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