From Wikipedia, the free encyclopedia
This is a list of named linear ordinary differential equations.
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
|
![{\displaystyle +\left[{\frac {\alpha \alpha '(a-b)(a-c)}{z-a}}+{\frac {\beta \beta '(b-c)(b-a)}{z-b}}+{\frac {\gamma \gamma '(c-a)(c-b)}{z-c}}\right]{\frac {w}{(z-a)(z-b)(z-c)}}=0}](http://178.128.105.246/cars-https-wikimedia.org/api/rest_v1/media/math/render/svg/edd0b3392ef2f62214eac8d4b1c54c285d45912d)
|
|
Quantum harmonic oscillator
|
2
|
|
Quantum mechanics
|
Sturm-Liouville
|
2
|
|
Applied mathematics
|