John D. Cook • 8/1/2026

Why polynomial coefficients?

This article discusses the significance of second order linear differential equations with polynomial coefficients, a class of ODEs that frequently arises from separating PDEs in physics. The author notes that while this topic is often overlooked in standard curricula, it is crucial because common PDEs like Helmholtz and Laplace equations reduce to such ODEs in various coordinate systems. The article references Kristensson's book for a deeper explanation and highlights the gap between undergraduate and graduate education regarding this subject.

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#Differential Equations #Second Order Odes #Polynomial Coefficients