Generating some linear second-order differential equations with undetermined coefficients by Linearly combining Frobenius and Legendre differential equations - Shahawe A. I. Daw, Essa S. Najem, Haniyah A. M. Saed (Journal of Pure & Applied Sciences, 2019)
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.....