A Treatise on Differential Equations |
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Page iii
... THE QUEEN'S UNIVERSITY , IRELAND , HONORARY MEMBER OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY . THIRD EDITION . London : MACMILLAN AND CO . 1872 . [ All Rights reserved . ] 1 PREFACE . I HAVE endeavoured , in the following.
... THE QUEEN'S UNIVERSITY , IRELAND , HONORARY MEMBER OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY . THIRD EDITION . London : MACMILLAN AND CO . 1872 . [ All Rights reserved . ] 1 PREFACE . I HAVE endeavoured , in the following.
Page x
... St John's College , as well as by myself ; and I trust that few misprints or errors will now be found in the volume . ST JOHN'S COLLEGE , CAMBRIDGE , October , 1865 . I. TODHUNTER . CONTENTS . CHAPTER I. OF THE NATURE AND ORIGIN OF.
... St John's College , as well as by myself ; and I trust that few misprints or errors will now be found in the volume . ST JOHN'S COLLEGE , CAMBRIDGE , October , 1865 . I. TODHUNTER . CONTENTS . CHAPTER I. OF THE NATURE AND ORIGIN OF.
Page 66
... ( Cambridge Mathematical Journal , Vol . IV . p . 241. First Series . ) х Suppose M and N to be homogeneous functions of x and of the degree n . Then we may write M = x " ¤ ( v ) , N = x ” ¥ ( v ) У where v stands for · х Hence Mdx + Ndy ...
... ( Cambridge Mathematical Journal , Vol . IV . p . 241. First Series . ) х Suppose M and N to be homogeneous functions of x and of the degree n . Then we may write M = x " ¤ ( v ) , N = x ” ¥ ( v ) У where v stands for · х Hence Mdx + Ndy ...
Page 121
... Cambridge Philosophical Transactions , Vol . x . ] 4. There are certain cases in which differential equations of the first order can be solved without the resolution of the first member into its component factors . Of these the most ...
... Cambridge Philosophical Transactions , Vol . x . ] 4. There are certain cases in which differential equations of the first order can be solved without the resolution of the first member into its component factors . Of these the most ...
Page 182
... Cambridge Philosophical Society , Vol . IX . Part II . ) . Geometrical illustrations will be found in the memoir referred to . EXERCISES . 1. The complete primitive of a differential equation is y + c = √ ( x2 + y2 - a ) , where c is ...
... Cambridge Philosophical Society , Vol . IX . Part II . ) . Geometrical illustrations will be found in the memoir referred to . EXERCISES . 1. The complete primitive of a differential equation is y + c = √ ( x2 + y2 - a ) , where c is ...
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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
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