A Treatise on Differential Equations, Volume 1 |
From inside the book
Results 1-5 of 56
Page
... exact differential coefficient . 28. Shew that y2 + ( 2xy - 1 ) dy dx d'y dy + x + x2 = dx2 dx3 = 0 is an exact differential equation , and deduce a first integral . d'y • 29. The equation + a2y dx2 ( y2 + x2 ) 2 = 0 becomes integrable ...
... exact differential coefficient . 28. Shew that y2 + ( 2xy - 1 ) dy dx d'y dy + x + x2 = dx2 dx3 = 0 is an exact differential equation , and deduce a first integral . d'y • 29. The equation + a2y dx2 ( y2 + x2 ) 2 = 0 becomes integrable ...
Page viii
... exact , and the more complete , that study of things has been , the more likely shall we be to employ with advantage all instru- mental aids and appliances . But although I have , for the reasons above mentioned , treated of symbolical ...
... exact , and the more complete , that study of things has been , the more likely shall we be to employ with advantage all instru- mental aids and appliances . But although I have , for the reasons above mentioned , treated of symbolical ...
Page xi
... . 23 CHAPTER III . EXACT DIFFERENTIAL EQUATIONS OF THE FIRST DEGREE 47 General criterion , 47. Mode of solution , 50. Practical simplifica- tions , 52. Exercises , 53 . CHAPTER IV . ON THE INTEGRATING FACTORS OF THE DIFFERENTIAL.
... . 23 CHAPTER III . EXACT DIFFERENTIAL EQUATIONS OF THE FIRST DEGREE 47 General criterion , 47. Mode of solution , 50. Practical simplifica- tions , 52. Exercises , 53 . CHAPTER IV . ON THE INTEGRATING FACTORS OF THE DIFFERENTIAL.
Page xiii
... differential coefficient present , 211 . dry dan dxn 212 . dry ' dn - 2y dxn dxn- 214. Homogeneous equa- tions , 215. Exact equations , 222. Miscellaneous methods and examples , 226. Singular integrals , 229. Exercises , 234 . CHAPTER ...
... differential coefficient present , 211 . dry dan dxn 212 . dry ' dn - 2y dxn dxn- 214. Homogeneous equa- tions , 215. Exact equations , 222. Miscellaneous methods and examples , 226. Singular integrals , 229. Exercises , 234 . CHAPTER ...
Page 7
... exact differential , = ху sin x + c ....... .. ( 12 ) . ......... ...... The result is termed the solution , or , still more definitely , the general solution of the equation . It involves an arbitrary constant , c , by giving ...
... exact differential , = ху sin x + c ....... .. ( 12 ) . ......... ...... The result is termed the solution , or , still more definitely , the general solution of the equation . It involves an arbitrary constant , c , by giving ...
Other editions - View all
Common terms and phrases
2ndly algebraic arbitrary constant arbitrary function assume C₁ C₂ Cambridge Chap Chapter College complete primitive condition corresponding Crown 8vo curve deduce degree derived determined differential coefficients dp dy dv dv dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dz Edition eliminating equa exact differential expressed Extra fcap fcap finite given equation Hence homogeneous functions Illustrations independent variable infinite integrating factor involving Mdx+Ndy method Mx+Ny obtained ordinary differential equations P₁ partial differential equation particular integral primitive equation Professor Prop reduced relation represent respect result satisfied second member second order Shew singular solution substituting suppose Taylor's theorem theorem tion transformation V₁ whence y₁ аф
Popular passages
Page 32 - Flower (WH) — AN INTRODUCTION TO THE OSTEOLOGY OF THE MAMMALIA. Being the Substance of the Course of Lectures delivered at the Royal College of Surgeons of England in 1870.
Page 47 - 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.
Page 47 - HOLE— A GENEALOGICAL STEMMA OF THE KINGS OF ENGLAND AND FRANCE. By the Rev. C. HOLE. On Sheet, is. JOHNSON'S LIVES OF THE POETS. The Six Chief Lives (Milton, Dryden, Swift, A'ddison, Pope, Gray), with Macaulay's "Life of Johnson.
Page 41 - EDUCATIONAL TIMES. YONGE (CHARLOTTE M.)— A PARALLEL HISTORY OF FRANCE AND ENGLAND : consisting of Outlines and Dates. By CHARLOTTE M. YONGE, Author of "The Heir of Redclyffe,
Page 18 - PRITCHARD (GS)— NOTE-BOOK ON PRACTICAL SOLID OR DESCRIPTIVE GEOMETRY. Containing Problems with help for Solutions. By JH EDGAR, MA, Lecturer on Mechanical Drawing at the Royal School of Mines, and GS PRITCHARD. New Edition, revised and enlarged. Globe 8vo. 3^.
Page 38 - FREEMAN (EDWARD A.)— OLD-ENGLISH HISTORY. By EDWARD A. FREEMAN, DCL, LL.D., late Fellow of Trinity College, Oxford. With Five Coloured Maps. New Edition. Extra fcap. 8vo. half-bound.
Page 26 - SOLID GEOMETRY AND CONIC SECTIONS. With Appendices on Transversals and Harmonic Division. For the Use of Schools. By JM WILSON, MA New Edition. Extra fcap. 8vo. 3*.
Page 45 - WILSON— THE BIBLE STUDENT'S GUIDE to the more Correct Understanding of the English Translation of the Old Testament, by reference to the original Hebrew. By WILLIAM WILSON, DD, Canon of Winchester, late Fellow of Queen's College, Oxford. Second Edition, carefully revised. 4to. cloth. 25*. YONGE (CHARLOTTE M.)— SCRIPTURE READINGS FOR SCHOOLS AND FAMILIES. By CHARLOTTE M. YONGE, Author of "The Heir of Redclyffe.
Page 42 - Morte d'Arthur.— SIR THOMAS MALORY'S BOOK OF KING ARTHUR AND OF HIS NOBLE KNIGHTS OF THE ROUND TABLE. The original Edition of CAXTON, revised for Modern Use. With an Introduction by Sir EDWARD STRACHEY, Bart. pp. xxxvii., 509. "It is with perfect confidence that we recommend this edition of the old romance to every class of readers.
Page 30 - LOGIC. ELEMENTARY LESSONS IN LOGIC; Deductive and Inductive, with copious Questions and Examples, and a Vocabulary of Logical Terms. By W. STANLEY JEVONS, MA, Professor of Political Economy in University College, London. New Edition. Fcap. 8vo. 3*. 6d. " Nothing can be better for a school-book. "-^-GUARDIAN. "A manual alike simple, interesting, and scientific."— ATHHN/UJH.