List of nonlinear ordinary differential equations

A–F

Name Order Equation Applications
Abel's differential equation of the first kind 1 Mathematics
Abel's differential equation of the second kind 1 Mathematics
Bellman's equation or Emden-Fowler's equation 2 Mathematics
Bernoulli equation 1 Mathematics
Besant-Rayleigh-Plesset equation 2 Fluid dynamics
Blasius equation 3 Blasius boundary layer
Chandrasekhar equation 2 Astrophysics
Chandrasekhar's white dwarf equation 2 Astrophysics
Chrystal's equation 1 Mathematics
Clairaut's equation 1 Mathematics
D'Alembert's equation 1 Mathematics
Darboux equation 1 Mathematics
De Boer-Ludford equation 2 Plasma physics
Duffing equation 2 Oscillators
Emden equation 2 Astrophysics
Euler's differential equation 1 Mathematics
Falkner–Skan equation 3 Falkner–Skan boundary layer

G–K

Name Order Equation Applications
Ivey's equation 2
Jacobi's differential equation 1 Mathematics
Kiddler equation 2 Flow through porous medium
Krogdahl equation 2 Stellar pulsation

L–Q

Name Order Equation Applications
Lane–Emden equation 2 Astrophysics
Langmuir equation 2 Environmental Engineering
Langmuir-Blodgett equation 2
Langmuir-Boguslavski equation 2
Liñán's equation 2 Combustion
Painlevé I transcendent 2 Mathematics
Painlevé II transcendent 2 Mathematics
Painlevé III transcendent 2 Mathematics
Painlevé IV transcendent 2 Mathematics
Painlevé V transcendent 2 Mathematics
Painlevé VI transcendent 2 Mathematics
Poisson-Boltzmann equation 2

R–Z

Name Order Equation Applications
Rayleigh equation 2
Riccati equation 1 Mathematics
Stuart–Landau equation 1 Hydrodynamic stability
Thomas–Fermi equation 2 Quantum mechanics[1]
Van der Pol equation 2 Oscillators

References

  1. Davis, Harold Thayer. Introduction to nonlinear differential and integral equations. Courier Corporation, 1962.
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