A Treatise on Differential Equations |
From inside the book
Results 1-5 of 79
Page 24
... satisfied . Conversely , if this condition be identically satisfied , V will be expressible as a function of v . 1st . For suppose V = 4 ( v ) . Then dV___dp ( v ) dv - dx dv dx ' = dV_do ( v ) dv dy dv dy Multiplying the first equation ...
... satisfied . Conversely , if this condition be identically satisfied , V will be expressible as a function of v . 1st . For suppose V = 4 ( v ) . Then dV___dp ( v ) dv - dx dv dx ' = dV_do ( v ) dv dy dv dy Multiplying the first equation ...
Page 26
... satisfied , that equation reduces to dv dy = 0 , whence Vis expressible as a function of v . dy 2. The equation M + N = 0 always involves the existence dx of a primitive relation between x and y of the form f ( x , y ) = c , in which c ...
... satisfied , that equation reduces to dv dy = 0 , whence Vis expressible as a function of v . dy 2. The equation M + N = 0 always involves the existence dx of a primitive relation between x and y of the form f ( x , y ) = c , in which c ...
Page 47
... satisfied , the primitive may be found . 2ndly , To ascertain whether , when those conditions are not satisfied , it is possible to discover a factor by which the equa- tion Mdx + Ndy = 0 being multiplied , its first member will become ...
... satisfied , the primitive may be found . 2ndly , To ascertain whether , when those conditions are not satisfied , it is possible to discover a factor by which the equa- tion Mdx + Ndy = 0 being multiplied , its first member will become ...
Page 48
... satisfy the equation ( 2 ) . Integrating this equation relatively to x alone ( since the dV differentiation in is relative to x alone ) , we have dx V = Mdx + C ................. = √ Mdx . ( 6 ) , C being a quantity which is constant ...
... satisfy the equation ( 2 ) . Integrating this equation relatively to x alone ( since the dV differentiation in is relative to x alone ) , we have dx V = Mdx + C ................. = √ Mdx . ( 6 ) , C being a quantity which is constant ...
Page 49
... satisfy the equation ( 3 ) . Sub- stituting in that equation the value of V given in ( 7 ) , we have df Mdx , do ( y ) Therefore Whence + dy аф ( у ) dy = N = N. dy df Mdx dy - df Mdx N. Ida ) dy + ......... ( 3 ) = √ ( 1 dy ( 8 ) , C ...
... satisfy the equation ( 3 ) . Sub- stituting in that equation the value of V given in ( 7 ) , we have df Mdx , do ( y ) Therefore Whence + dy аф ( у ) dy = N = N. dy df Mdx dy - df Mdx N. Ida ) dy + ......... ( 3 ) = √ ( 1 dy ( 8 ) , C ...
Other editions - View all
Common terms and phrases
2ndly algebraic arbitrary constant arbitrary function assume C₁ C₂ Cambridge Chap Chapter cloth complete primitive condition Crown 8vo curve deduce determined differential coefficients dp dq dp dy dt dt dv dv dv dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dz Edition EDUCATIONAL BOOKS elementary eliminating equa exact differential example expressed fcap finite given equation gives Hence homogeneous functions independent variable integrating factor involving Mdx+Ndy method Mx+Ny obtained ordinary differential equations partial differential equation particular integral primitive equation problem reduced relation represent respect result satisfied second member second order shew singular solution substituting suppose theorem tion transformation TREATISE whence X₁ Y₁ аф
Popular passages
Page 19 - ELEMENTARY TREATISE ON PARTIAL DIFFERENTIAL EQUATIONS. Designed for the Use of Students in the Universities. With Diagrams. Second Edition. Crown 8vo. $s. 6d. ON THE ALGEBRAICAL AND NUMERICAL THEORY OF ERRORS OF OBSERVATIONS AND THE COMBINATION OF OBSERVATIONS.
Page 7 - HODGSON -MYTHOLOGY FOR LATIN VERSIFICATION. A brief Sketch of the Fables of the Ancients, prepared to be rendered into Latin Verse for Schools.
Page 7 - MARSHALL — A TABLE OF IRREGULAR GREEK VERBS, classified according to the arrangement of Curtius
Page 20 - ON SOUND AND ATMOSPHERIC VIBRATIONS. With the Mathematical Elements of Music. Designed for the Use of Students in the University. Second Edition, Revised and Enlarged. Crown 8vo.
Page 66 - A GENERAL SURVEY OF THE HISTORY OF THE CANON OF THE NEW TESTAMENT DURING THE fIRST FOUR CENTURIES. Fourth Edition. With Preface on "Supernatural Religion.
Page 4 - ARISTOTLE— AN INTRODUCTION TO ARISTOTLE'S RHETORIC. With Analysis, Notes and Appendices. By EM COPE, Fellow and Tutor of Trinity College, Cambridge, 8vo.
Page 25 - Ferrers. — AN ELEMENTARY TREATISE ON TRILINEAR CO-ORDINATES, the Method of Reciprocal Polars, and the Theory of Projectors. By the Rev. NM FERRERS, MA, Fellow and Tutor of Gonville and Caius College, Cambridge.
Page 29 - Prelector of St. John's College, Cambridge. AN ELEMENTARY TREATISE ON MECHANICS. For the Use of the Junior Classes at the University and the Higher Classes in Schools.
Page 28 - KITCHENER— A GEOMETRICAL NOTE-BOOK, containing Easy Problems in Geometrical Drawing preparatory to the Study of Geometry. For the use of Schools.
Page 49 - The object of the author in this book is to present the philosophy of Chemistry in such a form that it can be made with profit the subject of College recitations, and furnish the teacher with the means of testing the student's faithfulness and ability.