Search results
Results from the WOW.Com Content Network
Irregular odes further break down the ode's formal conventions. They are sometimes called Cowleyan odes after the English Enlightenment poet Abraham Cowley, who revived the form in England with his publication of fifteen Pindarique Odes in 1656. Though this title derives from Pindar, it is a misunderstanding of the Pindaric ode on Cowley's part.
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
The few non-linear ODEs that can be solved explicitly are generally solved by transforming the equation into an equivalent linear ODE (see, for example Riccati equation). [5] Some ODEs can be solved explicitly in terms of known functions and integrals.
1.6 Ordinary Differential Equations (ODEs) 1.7 Riemannian geometry. 2 Physics. Toggle Physics subsection. 2.1 Astrophysics. 2.2 Classical mechanics. 2.3 Electromagnetism.
A number of schemes have been suggested, but one principle of arrangement appears to be that there is a symmetry (that is, a chiastic or ring structure) between the first and second half of the collection, so that several of the odes in the first half have a thematic or phrasal connection with corresponding odes in the second half. [31] For ...
For an arbitrary system of ODEs, a set of solutions (), …, are said to be linearly-independent if: + … + = is satisfied only for = … = =.A second-order differential equation ¨ = (,, ˙) may be converted into a system of first order linear differential equations by defining = ˙, which gives us the first-order system:
(Figure 2) Illustration of numerical integration for the equation ′ =, = Blue is the Euler method; green, the midpoint method; red, the exact solution, =. The step size is =
The 'Ode to a Nightingale,' for example, is a less 'perfect' though a greater poem." [ 30 ] Charles Patterson argued the relationship of "Ode on a Grecian Urn" as the greatest 1819 ode of Keats: "The meaningfulness and range of the poem, along with its controlled execution and powerfully suggestive imagery, entitle it to a high place among ...