Differential equation
Summary
A differential equation is an equation that relates an unknown function to one or more of its derivatives. A solution is a function that makes the equation true at each point of its domain. If the unknown function depends on one variable, the equation is an ordinary differential equation. If it depends on several variables and the equation has partial derivatives, it is a partial differential equation.
Remarks
The order of a differential equation is the highest order of a derivative in it. The equation is a differential equation of order . Its solutions are the functions with a constant . Differential equations describe how a quantity changes. Many laws of physics, biology and economics have this form.
Explanations
L1 human
An ordinary equation asks for a number, but a differential equation asks for a function. The equation gives a rule for the rate of change of the function. For example, says that the function grows at a rate equal to its own value.
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- edge specializes both: the more general notions and the special cases (0 of 1)
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- Non-uniqueness for a non-Lipschitz equation 00K7ASZ1PR
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- Lotka–Volterra equations 00Y5QZ82AA
- Integral equation form of an initial value problem 015KK993C5
- Maximal solution 019VSXSFMQ
- Periodic orbit 01DSNP0B4R
- Integrating factor 01THH3Y3YP
- Uniqueness of solutions for Lipschitz vector fields 025PKW8AMR
- Flow of a vector field 02903SSA48
- Newton's law of cooling 02HB5F40VR
- Reduction of order 02SRXDAM3X
- C^1 vector fields satisfy the Picard–Lindelöf hypotheses 03Z9V0Y78A
- Lyapunov function 04P7B5XC22
- Solution of an ordinary differential equation 04SW7WECS8
- Phase plane 05VDGH129F
- Asymptotic stability 05Y1JAM3Y5
- LaSalle's invariance principle 0659J5X7B5
- Solution formula for linear first-order equations 06B9W45XV0
- Initial value problem 075VBY4K4X
- Autonomous system 07BNRFQ0PJ
- Phase line 081QSEAGEY
- Power series solution 08RT9GDDPQ
- Explicit and implicit differential equations 08WWTN738R
- An iterate of the Picard operator is a contraction 08XDXP86XE
- Eigenvalue method for linear systems 08ZWFDJP3H
- Lyapunov stability 092S6VBECQ
- Peano existence theorem 098YP831QY
- Order of a differential equation 09M2RDB61G
- Liouville's formula 09PS3S0EF6
- Linearisation at an equilibrium 09ZWYRQ41J
- Linear equation with constant coefficients 0A6PGTTP2A
- System of linear differential equations 0A6QZ367GX
- Solutions for complex conjugate roots 0BEZX8F2XW
- Global existence for globally Lipschitz vector fields 0BFD3A6CRH
- Trajectory 0BVT6VSB3S
- Hamiltonian system 0C2AKPDCD9
- Hyperbolic equilibrium point 0C5PREPZWG
- Logistic equation 0CC4VC7KR3
- Integrating factor for a non-exact equation 0CX86CR8JV
- Singular solution 0CZA0NCFWP
- Riccati equation 0E1ZZBHZ3Z
- Blow-up in finite time 0E4GXX7SJP
- Exact equation 0EC7AGJ0PX
- Limit cycle 0EERDDPSVT
- Homogeneous linear equation 0EQZSAB9EC
- Poincaré–Bendixson theorem 0EW1X61ZT1
- Superposition principle 0F2VBPXNP9
- Continuous dependence on initial data 0G3DBXRRQJ
- Equilibrium point 0G4X36AE0X
- General solution of an inhomogeneous linear equation 0GHWEH6H15
- Solution space of a homogeneous linear equation has dimension n 0GK68PZ6KH
- Fundamental system of solutions 0H4KNNCHPY
- Solutions for distinct real roots 0HJ0HDA6W7
- Solutions for repeated roots 0HRVY67CNV
- Lyapunov's stability theorem 0J6A752DTZ
- Picard–Lindelöf hypotheses 0J7HF2PF1H
- Euler method 0JARTXX4XP
- Underdamped 0JJ6GDDE7Z
- Solving initial value problems with the Laplace transform 0K3HFZJK5Q
- Homogeneous first-order equation 0K4ZWTFSV5
- Wronskian test for linear independence of solutions 0MHE4B1QCQ
- Fundamental matrix 0MQ24RBG93
- Test for exactness 0MSCQNFTM8
- Classification of equilibria of planar linear systems 0N7ATVF2X8
- Picard–Lindelöf theorem 0P6KRD5B7A
- Ordinary differential equation 0P97V20RW7
- Linear differential equation of order n 0PB7K8M7FG
- Characteristic equation 0QDXMG46QW
- Picard iteration 0RJ5NHWYTP
- Slope field 0RKQQQACY7
- Damped harmonic oscillator 0RNXVVTJTJ
- Variation of constants formula for linear systems 0S1KG0XE40
- Hartman–Grobman theorem 0S8WX8A4V9
- Pendulum equation 0SHPXM2HWH
- Stability of linear systems via eigenvalues 0SKVEMXJWF
- General solution and particular solution 0SKYFQAFYD
- First integral 0SS1P1YC9A
- Phase portrait 0T3GK0XCBC
- Clairaut's equation 0T6D4PE51C
- Reduction of a higher-order equation to a first-order system 0TH9CPW3VS
- Separable equation 0V4E623THY
- Abel's identity 0VGWKX2JHB
- Homogeneous linear system with constant coefficients 0VJF99CZ0Z
- Time translation of solutions of an autonomous system 0WA7ZR95V4
- Cauchy–Euler equation 0WDNRBXX7K
- Nullcline 0WW060JR6P
- Forced oscillation and resonance 0X4NT20S3G
- Method of undetermined coefficients 0XRB469Z32
- Variation of parameters 0Y6TH5PQVS
- Matrix exponential as the solution of a linear system 0YC8JT513J
- Harmonic oscillator 0YG0ZJPTWG
- Linear first-order equation 0Z3YKRQZ48
- Bernoulli equation 0ZB84QCDKR
Sources
- Web https://en.wikipedia.org/wiki/Differential_equation, lead section
What links here
Used by
- Ordinary differential equation 0P97V20RW7