A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Σελίδα 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 ...
Σελίδα 2
... independent variable æ , it is ax proposed to determine the most general relation between y and x . Expressing the given relation in the form dy dx = $ ( x ) the relation sought is exhibited in the form y = [ $ ( x ) dx + c . ( 1 ) , In ...
... independent variable æ , it is ax proposed to determine the most general relation between y and x . Expressing the given relation in the form dy dx = $ ( x ) the relation sought is exhibited in the form y = [ $ ( x ) dx + c . ( 1 ) , In ...
Σελίδα 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 ...
Σελίδα 4
... independent variable x , the dependent variable dy dx and the differential coefficient are all involved ; but , dy while in the previous examples appears only in the first dx degree , in the present one it appears in the second degree ...
... independent variable x , the dependent variable dy dx and the differential coefficient are all involved ; but , dy while in the previous examples appears only in the first dx degree , in the present one it appears in the second degree ...
Σελίδα 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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2ndly algebraic arbitrary constants arbitrary function assume C₁ C₂ Chap Chapter complete primitive condition Crown 8vo curve deduce derived determined differential coefficients dp dp dp dq dp dy dt dt dv du dv dv dv dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dy dz dz Edition eliminating equa exact differential expressed fcap finite given equation Hence homogeneous functions independent variable integrating factor involving method Mx+Ny obtained ordinary differential equations P₁ partial differential equation particular integral pdx+qdy primitive equation reduced relation represent respect result satisfied second member second order Shew shewn singular solution substituting suppose theorem tion transformation whence X₁ y₁