This is a list of named linear ordinary differential equations.
A–Z
Name Order Equation Applications Airy 2 Optics Bessel 2 Wave propagation Cauchy-Euler n Chebyshev 2 Orthogonal polynomials Damped harmonic oscillator 2 Damping Frenet-Serret 1 Differential geometry General Laguerre 2 Hydrogen atom General Legendre 2 Harmonic oscillator 2 Simple harmonic motion Heun 2 Hill 2 , (f periodic) Physics Hypergeometric 2 Kummer 2 Laguerre 2 Legendre 2 Orthogonal polynomials Matrix 1 Picard-Fuchs 2 Elliptic curves Riemann 2 Quantum harmonic oscillator 2 Quantum mechanics Sturm-Liouville 2 Applied mathematics