A Treatise on Differential Equations, Τόμος 1Macmillan, 1872 - 85 σελίδες |
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Σελίδα viii
... respect to the sources from which information has been drawn , it is proper to mention that , on questions re- lating to the theory of differential equations , my obligations are greatest to Lagrange , Jacobi , Cauchy , and , of living ...
... respect to the sources from which information has been drawn , it is proper to mention that , on questions re- lating to the theory of differential equations , my obligations are greatest to Lagrange , Jacobi , Cauchy , and , of living ...
Σελίδα 3
... respect to which those differential coefficients have been formed . Thus an equation such as ( 2 ) or ( 3 ) , involving no other differential coefficients than & c , is an ordinary dif- dy day dx ' dx2 , ferential equation , in which x ...
... respect to which those differential coefficients have been formed . Thus an equation such as ( 2 ) or ( 3 ) , involving no other differential coefficients than & c , is an ordinary dif- dy day dx ' dx2 , ferential equation , in which x ...
Σελίδα 4
... respect to x ; the presence of the last element only , viz . the differential coefficient , being essen- tial ( Art . 1 ) . The two following equations , in addition to those already given , will exemplify some of the chief varieties of ...
... respect to x ; the presence of the last element only , viz . the differential coefficient , being essen- tial ( Art . 1 ) . The two following equations , in addition to those already given , will exemplify some of the chief varieties of ...
Σελίδα 14
... respect to x , and regarding y as a function of x , we obtain directly , or by elimination of c1 , an equation of the first order of the form dy $ 1 ( X , Y , Z , C2 , C3 , ... C „ ) = 0 . dx ' Differentiating this equation with respect ...
... respect to x , and regarding y as a function of x , we obtain directly , or by elimination of c1 , an equation of the first order of the form dy $ 1 ( X , Y , Z , C2 , C3 , ... C „ ) = 0 . dx ' Differentiating this equation with respect ...
Σελίδα 47
... that Mdx + Ndy is an exact differential . It is that M and N are partial differential coefficients with respect to x and y , —that there exists some function ( 47 ) CHAPTER III EXACT DIFFERENTIAL EQUATIONS OF THE FIRST DEGREE.
... that Mdx + Ndy is an exact differential . It is that M and N are partial differential coefficients with respect to x and y , —that there exists some function ( 47 ) CHAPTER III EXACT DIFFERENTIAL EQUATIONS OF THE FIRST DEGREE.
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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