A Treatise on Differential EquationsMacmillan, 1865 - 496 páginas |
Dentro del libro
Resultados 1-5 de 50
Página 3
... becomes du dk = C. In applying this theory to the reduction of the general solution ( 2 ) in the case in which m1 = m2 , it must be observed that the numerator of the first member is the same function of m ,, x , y , as the denominator ...
... becomes du dk = C. In applying this theory to the reduction of the general solution ( 2 ) in the case in which m1 = m2 , it must be observed that the numerator of the first member is the same function of m ,, x , y , as the denominator ...
Página 4
... becomes on putting C for d dm log ( m ) = C , • C gn d 1 or • dm am -- a " log { ( am — a ' ) ( x + my ) + cm − c ' } = C. - 3. [ The next Article seems to have been intended to ap- pear in the enlarged form of Chap . II .; but I ...
... becomes on putting C for d dm log ( m ) = C , • C gn d 1 or • dm am -- a " log { ( am — a ' ) ( x + my ) + cm − c ' } = C. - 3. [ The next Article seems to have been intended to ap- pear in the enlarged form of Chap . II .; but I ...
Página 14
... It would not there- fore be infinite . Hence we conclude that would not become dp dy infinite for a particular primitive in the strict sense of that term , i . e . for a solution derived 14 [ CH . XXI . ADDITIONS TO CHAPTER VIII .
... It would not there- fore be infinite . Hence we conclude that would not become dp dy infinite for a particular primitive in the strict sense of that term , i . e . for a solution derived 14 [ CH . XXI . ADDITIONS TO CHAPTER VIII .
Página 15
... become infinite not only when ( x , c ) = 0 , but also when ( x , c ) = infinite , we see that a relation between y dp ... becomes infinite when y = 0. As this involves y and satisfies the differential equation it is a singular solution ...
... become infinite not only when ( x , c ) = 0 , but also when ( x , c ) = infinite , we see that a relation between y dp ... becomes infinite when y = 0. As this involves y and satisfies the differential equation it is a singular solution ...
Página 17
... becomes infinite if x = 0 ; but this not involving y must be rejected . Again , it becomes infinite if y = 0 , and this proves to be a solution of the differential equation , the limiting value of the indeterminate function in the ...
... becomes infinite if x = 0 ; but this not involving y must be rejected . Again , it becomes infinite if y = 0 , and this proves to be a solution of the differential equation , the limiting value of the indeterminate function in the ...
Otras ediciones - Ver todas
Términos y frases comunes
arbitrary constants Cambridge Chap Chapter College complete primitive condition Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dF dF dp dF dx dFdF differential coefficients dp dF dp dp dx dp dq dp dy dp₁ dq dp dv dv dx dp dp dx dx dx dy dy dx dz dx₁ dx² dy dp dy dx dy dz dz dy dz dz Edition eliminate equa Eton College expression Extra fcap factor function given equation Hence J. P. MAHAFFY Jacobi Last Multiplier linear partial differential m₁ memoir ordinary differential equations Owens College P₁ partial differential equations particular integral Professor Boole reduced represent result revised School shewn singular solution system of ordinary theorem theory tion transformation u₁ u₂ values vanish whence X₁ Y₁ аф
Pasajes populares
Página 43 - THE BIBLE IN THE CHURCH. A Popular Account of the Collection and Reception of the Holy Scriptures in the Christian Churches. New Edition.
Página 18 - With Notes and Illustrations. Also a collection of Problems, principally intended as Examples of Newton's Methods. By PERCIVAL FROST, MA Third Edition. 8vo.
Página 50 - Book VI. is fitted for higher Classes, and as an Introduction to English Literature. " They are far above any others that have appeared both in form and substance. . . . The editor of the present series has rightly seen that reading books must . aim chiefly at giving to the pupils the power of accurate, and, if possible, apt and skilful expression ; at cultivating in them a good literary taste, and at arousing a desire of further reading.
Página 45 - HALES— LONGER ENGLISH POEMS, with Notes, Philological and Explanatory, and an Introduction on the Teaching of English. Chiefly for Use in Schools. Edited by JW HALES, MA, Professor of English Literature at King's College, London.
Página 17 - HEMMING— AN ELEMENTARY TREATISE ON THE DIFFERENTIAL AND INTEGRAL CALCULUS, for the Use of Colleges and Schools. By GW HEMMING, MA, Fellow of St. John's College, Cambridge. Second Edition, with Corrections and Additions. 8vo.
Página 25 - They are wonderfully clear and lucid in their instruction, simple in style, and admirable in plan. , — EDUCATIONAL TIMES.
Página 45 - Hole. — A GENEALOGICAL STEMMA OF THE KINGS OF ENGLAND AND FRANCE. By the Rev. C. HOLE, MA, Trinity College, Cambridge. On Sheet, Is.
Página 33 - NATURE SERIES. THE SPECTROSCOPE AND ITS APPLICATIONS. By J. NORMAN LOCKYER, FRS With Coloured Plate and numerous Illustrations. Second Edition. Crown 8vo. 3*. 6d. THE ORIGIN AND METAMORPHOSES OF INSECTS.
Página 7 - HODGSON -MYTHOLOGY FOR LATIN VERSIFICATION. A brief Sketch of the Fables of the Ancients, prepared to be rendered into Latin Verse for Schools.
Página 13 - TREATISE ON GEOMETRICAL OPTICS. Adapted for the use of the Higher Classes in Schools. By OSMUND AIRY, BA, one of the Mathematical Masters in Wellington College. Extra fcap.