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Examples of differential equations; Autonomous system (mathematics) Picard–Lindelöf theorem; Peano existence theorem; Carathéodory existence theorem; Numerical ordinary differential equations; Bendixson–Dulac theorem; Gradient conjecture; Recurrence plot; Limit cycle; Initial value problem; Clairaut's equation; Singular solution ...
These include differential equations, manifolds, Lie groups, and ergodic theory. [4] This article gives a summary of the most important of these. This article lists equations from Newtonian mechanics, see analytical mechanics for the more general formulation of classical mechanics (which includes Lagrangian and Hamiltonian mechanics).
Differential equations play a prominent role in many scientific areas: mathematics, physics, engineering, chemistry, biology, medicine, economics, etc. This list presents differential equations that have received specific names, area by area.
The order of the differential equation is the highest order of derivative of the unknown function that appears in the differential equation. For example, an equation containing only first-order derivatives is a first-order differential equation, an equation containing the second-order derivative is a second-order differential equation, and so on.
Differential equations are prominent in many scientific areas. Nonlinear ones are of particular interest for their commonality in describing real-world systems and how much more difficult they are to solve compared to linear differential equations.
Physics: Hypergeometric: 2 ... List of nonlinear partial differential equations; List of named differential equations; References This page was last ...
Partial differential equation. Nonlinear partial differential equation. list of nonlinear partial differential equations; Boundary condition; Boundary value problem. Dirichlet problem, Dirichlet boundary condition; Neumann boundary condition; Stefan problem; Wiener–Hopf problem; Separation of variables; Green's function; Elliptic partial ...
Among ordinary differential equations, linear differential equations play a prominent role for several reasons. Most elementary and special functions that are encountered in physics and applied mathematics are solutions of linear differential equations (see Holonomic function ).