Ordinary differential equations Elementary methods of solution Concept
Linear differential equation of order n
Summary
A linear differential equation is an equation in which the unknown function and its derivatives occur linearly, with coefficients that are functions of the variable. Its solutions are a particular solution plus the solutions of the associated homogeneous equation, which form a vector space. See the definition.
Where this leads
26 pages build on this one.
- Operational calculus
- Spheroidal wave function
- Duhamel's integral
- Reduction of an initial value problem to a Volterra equation
- Irregular singularity
- Regular singular point
- Oscillation theory
- Heaviside operational calculus
- Hartman–Wintner theorem
- Picard–Vessiot extension
- Heun function
- Lamé function
- Kovacic's algorithm
- Mikusiński operational calculus
- Holonomic function
- Resonance
- Coulomb wave function
- Annihilator method
- Parabolic cylinder function
- Periodic boundary conditions
- Ordinary point and singular point
- Kummer's equation
- Sturm comparison theorem
- Sturm separation theorem
- Mathieu function
- Green's function
Further reading
About this page
| Tag | 0QQRP17Z7S |
|---|---|
| URI | m2://0QQRP17Z7S |
| Aliases | linear-differential-equation |
| Kind | concept |
| Writing | W1 stated |
| MSC | 34A30 |
| Specializes | Ordinary differential equation |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (1 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Special cases
- Cauchy–Euler equation
- Linear first-order equation
- Homogeneous linear equation
- Linear equation with constant coefficients
- Kummer's equation
Definitions
Used by
- Operational calculus
- Spheroidal wave function
- Duhamel's integral
- Reduction of an initial value problem to a Volterra equation
- Irregular singularity
- Regular singular point
- Oscillation theory
- Heaviside operational calculus
- Hartman–Wintner theorem
- Picard–Vessiot extension
- Heun function
- Lamé function
- Mikusiński operational calculus
- Holonomic function
- Resonance
- Coulomb wave function
- Annihilator method
- Parabolic cylinder function
- Periodic boundary conditions
- Ordinary point and singular point
- Kummer's equation
- Sturm comparison theorem
- Sturm separation theorem
- Mathieu function
- Green's function