Matches in SemOpenAlex for { <https://semopenalex.org/work/W2090978868> ?p ?o ?g. }
Showing items 1 to 52 of
52
with 100 items per page.
- W2090978868 endingPage "54" @default.
- W2090978868 startingPage "31" @default.
- W2090978868 abstract "If the operation of differentiation with regard to the independent variable x be denoted by the symbol D, and if ϕ (D) represent any function of D composed of integral powers positive or negative, or both positive and negative, it may easily be shown, that ϕ (D){ψ x. u } = ψ x. ϕ (D) u + ψ' x. ϕ' (D) u + ½ψ x. ϕ (D) u + 1/2.3 ψ' x. ϕ' (D) u + . . . (1.) and that ϕx .ψ(D) u = ψ(D){ ϕx. u } - ψ'(D){ ϕ'x. u } + ½ψ(D){ ϕx. u } - 1/2.3ψ'(D){ ϕ'x. u } + . . (2.) and these general theorems are expressions of the laws under which the operations of differentiation, direct and inverse, combine with those operations which are denoted by factors, functions of the independent variable. It will be perceived that the right-hand side of each of these equations is a linear differential expression; and whenever an expression assumes or can be made to assume either of these forms, its solution is determined; for the equations ϕ (D){ψ x. u } = P and ϕx . ψ(D) u = P are respectively equivalent to u = (ψ x ) -1 { ϕ (D)} -1 P and u = {ψ(D)} -1 (( ϕx ) -1 P)." @default.
- W2090978868 created "2016-06-24" @default.
- W2090978868 date "1848-12-31" @default.
- W2090978868 modified "2023-09-25" @default.
- W2090978868 title "II. On the solution of linear differential equations" @default.
- W2090978868 doi "https://doi.org/10.1098/rstl.1848.0002" @default.
- W2090978868 hasPublicationYear "1848" @default.
- W2090978868 type Work @default.
- W2090978868 sameAs 2090978868 @default.
- W2090978868 citedByCount "5" @default.
- W2090978868 countsByYear W20909788682015 @default.
- W2090978868 crossrefType "journal-article" @default.
- W2090978868 hasConcept C134306372 @default.
- W2090978868 hasConcept C13982400 @default.
- W2090978868 hasConcept C28826006 @default.
- W2090978868 hasConcept C33923547 @default.
- W2090978868 hasConcept C78045399 @default.
- W2090978868 hasConceptScore W2090978868C134306372 @default.
- W2090978868 hasConceptScore W2090978868C13982400 @default.
- W2090978868 hasConceptScore W2090978868C28826006 @default.
- W2090978868 hasConceptScore W2090978868C33923547 @default.
- W2090978868 hasConceptScore W2090978868C78045399 @default.
- W2090978868 hasLocation W20909788681 @default.
- W2090978868 hasOpenAccess W2090978868 @default.
- W2090978868 hasPrimaryLocation W20909788681 @default.
- W2090978868 hasRelatedWork W106941227 @default.
- W2090978868 hasRelatedWork W1547023645 @default.
- W2090978868 hasRelatedWork W1969042714 @default.
- W2090978868 hasRelatedWork W2038899271 @default.
- W2090978868 hasRelatedWork W2047532464 @default.
- W2090978868 hasRelatedWork W2063990599 @default.
- W2090978868 hasRelatedWork W2079178518 @default.
- W2090978868 hasRelatedWork W2340855652 @default.
- W2090978868 hasRelatedWork W2477503601 @default.
- W2090978868 hasRelatedWork W2483513174 @default.
- W2090978868 hasRelatedWork W2484153560 @default.
- W2090978868 hasRelatedWork W2490259958 @default.
- W2090978868 hasRelatedWork W2796221509 @default.
- W2090978868 hasRelatedWork W2796893429 @default.
- W2090978868 hasRelatedWork W2797904261 @default.
- W2090978868 hasRelatedWork W2802283138 @default.
- W2090978868 hasRelatedWork W2951602992 @default.
- W2090978868 hasRelatedWork W3002555443 @default.
- W2090978868 hasRelatedWork W608647825 @default.
- W2090978868 hasRelatedWork W2600409954 @default.
- W2090978868 hasVolume "138" @default.
- W2090978868 isParatext "false" @default.
- W2090978868 isRetracted "false" @default.
- W2090978868 magId "2090978868" @default.
- W2090978868 workType "article" @default.