A Treatise on Differential Equations |
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Page xi
... independent , 15. Cri- terion of derivation from a common primitive , 16. General form of equations thus related , 17. Geometrical illustrations , 18 . Exercises , 20 . PAGE 1 CHAPTER II . ON DIFFERENTIAL EQUATIONS OF THE FIRST ORDER ...
... independent , 15. Cri- terion of derivation from a common primitive , 16. General form of equations thus related , 17. Geometrical illustrations , 18 . Exercises , 20 . PAGE 1 CHAPTER II . ON DIFFERENTIAL EQUATIONS OF THE FIRST ORDER ...
Page 2
... independent variable x , it is proposed to determine the most general relation between y and x . Expressing the given relation in the form = dy = ( x ) dx . ( 1 ) , the relation sought is exhibited in the form y = [ $ ( x ) dz + c . φι ...
... independent variable x , it is proposed to determine the most general relation between y and x . Expressing the given relation in the form = dy = ( x ) dx . ( 1 ) , the relation sought is exhibited in the form y = [ $ ( x ) dz + c . φι ...
Page 3
... independent variable . 2ndly . Partial differential equations , characterized by the presence of partial differential coefficients , and therefore in- dicating the existence of two or more independent variables with respect to which ...
... independent variable . 2ndly . Partial differential equations , characterized by the presence of partial differential coefficients , and therefore in- dicating the existence of two or more independent variables with respect to which ...
Page 4
... independent variable x , the dependent variable dy y , and the differential coefficient are all involved ; but , dx dy while in the previous examples dx appears only in the first degree , in the present one it appears in the second ...
... independent variable x , the dependent variable dy y , and the differential coefficient are all involved ; but , dx dy while in the previous examples dx appears only in the first degree , in the present one it appears in the second ...
Page 6
... independent ; such reference being established through the medium of differential coefficients . Now the chief object of the study of differential equations is to enable us to determine whenever it is possible , and in the most 6 [ CH ...
... independent ; such reference being established through the medium of differential coefficients . Now the chief object of the study of differential equations is to enable us to determine whenever it is possible , and in the most 6 [ CH ...
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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
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