Name
|
Order
|
Equation
|
Application
|
Reference
|
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]
|