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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 ...
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.
Differential equations play an important role in modeling virtually every physical, technical, or biological process, from celestial motion, to bridge design, to interactions between neurons. Differential equations such as those used to solve real-life problems may not necessarily be directly solvable, i.e. do not have closed form solutions
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.
First order LTI systems are characterized by the differential equation + = where τ represents the exponential decay constant and V is a function of time t = (). The right-hand side is the forcing function f(t) describing an external driving function of time, which can be regarded as the system input, to which V(t) is the response, or system output.
Differential equations arise naturally in the physical sciences, in mathematical modelling, and within mathematics itself. For example, Newton's second law, which describes the relationship between acceleration and force, can be stated as the ordinary differential equation =.
Lane–Emden equation; Laser diode rate equations; Legendre's differential equation; Libroadrunner; Liénard equation; Liñán's equation; Liouville's formula; Lommel function; Lotka–Volterra equations; Lumped parameter model for the cardiovascular system
Euler equations; Fokker–Planck equation; Hamilton–Jacobi equation, Hamilton–Jacobi–Bellman equation; Heat equation; Laplace's equation. Laplace operator; Harmonic function; Spherical harmonic; Poisson integral formula; Klein–Gordon equation; Korteweg–de Vries equation. Modified KdV–Burgers equation; Maxwell's equations; Navier ...