Name | Order | Equation | Application | Reference |
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Abel's differential equation of the first kind | 1 |  | Class of differential equation which may be solved implicitly | [1] |
Abel's differential equation of the second kind | 1 |  | Class of differential equation which may be solved implicitly | [1] |
Bernoulli equation | 1 |  | Class of differential equation which may be solved exactly | [2] |
Binomial differential equation |  |  | Class of differential equation which may sometimes be solved exactly | [3] |
Briot-Bouquet Equation | 1 |  | Class of differential equation which may sometimes be solved exactly | [4] |
Cherwell-Wright differential equation | 1 | or the related form  | An example of a nonlinear delay differential equation; applications in number theory, distribution of primes, and control theory | [5] [6] [7] |
Chrystal's equation | 1 |  | Generalization of Clairaut's equation with a singular solution | [8] |
Clairaut's equation | 1 |  | Particular case of d'Alembert's equation which may be solved exactly | [9] |
d'Alembert's equation or Lagrange's equation | 1 |  | May be solved exactly | [10] |
Darboux equation | 1 |  | Can be reduced to a Bernoulli differential equation; a general case of the Jacobi equation | [11] |
Elliptic function | 1 |  | Equation for which the elliptic functions are solutions | [12] |
Euler's differential equation | 1 |  | A separable differential equation | [13] |
Euler's differential equation | 1 |  | A differential equation which may be solved with Bessel functions | [13] |
Jacobi equation | 1 |  | Special case of the Darboux equation, integrable in closed form | [14] |
Loewner differential equation | 1 |  | Important in complex analysis and geometric function theory | [15] |
Logistic differential equation (sometimes known as the Verhulst model) | 2 |  | Special case of the Bernoulli differential equation; many applications including in population dynamics | [16] |
Lorenz attractor | 1 |  | Chaos theory, dynamical systems, meteorology | [17] |
Nahm equations | 1 |  | Differential geometry, gauge theory, mathematical physics, magnetic monopoles | [18] |
Painlevé I transcendent | 2 |  | One of fifty classes of differential equation of the form ; the six Painlevé transcendents required new special functions to solve | [19] |
Painlevé II transcendent | 2 |  | One of fifty classes of differential equation of the form ; the six Painlevé transcendents required new special functions to solve | [19] |
Painlevé III transcendent | 2 |  | One of fifty classes of differential equation of the form ; the six Painlevé transcendents required new special functions to solve | [19] |
Painlevé IV transcendent | 2 |  | One of fifty classes of differential equation of the form ; the six Painlevé transcendents required new special functions to solve | [19] |
Painlevé V transcendent | 2 |  | One of fifty classes of differential equation of the form ; the six Painlevé transcendents required new special functions to solve | [19] |
Painlevé VI transcendent | 2 |  | All of the other Painlevé transcendents are degenerations of the sixth | [19] |
Rabinovich–Fabrikant equations | 1 |  | Chaos theory, dynamical systems | [20] |
Riccati equation | 1 |  | Class of first order differential equations that is quadratic in the unknown. Can reduce to Bernoulli differential equation or linear differential equation in certain cases | [21] |
Rössler attractor | 1 |  | Chaos theory, dynamical systems | [22] |