A Treatise on Differential Equations, Volumen1Macmillan and Company, 1877 - 496 páginas |
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Página 7
... equation . Thus if the given equation be dy OC da + y = cos x . . ( 11 ) , the following process of solution may be ... given differential equation . The term solution is still employed , even when the inte- gration necessary in order ...
... equation . Thus if the given equation be dy OC da + y = cos x . . ( 11 ) , the following process of solution may be ... given differential equation . The term solution is still employed , even when the inte- gration necessary in order ...
Página 8
George Boole. and the last result is called the solution of the given equation , although it involves an integration ... given primitive . If it involve c , then the elimination of c between it and the primitive will lead to the ...
George Boole. and the last result is called the solution of the given equation , although it involves an integration ... given primitive . If it involve c , then the elimination of c between it and the primitive will lead to the ...
Página 10
... from an equa- tion containing x and y with an arbitrary constant c , we can by differentiation , and elimination ( if necessary ) of that con- stant , obtain the differential equation of the first order , of which the given equation ...
... from an equa- tion containing x and y with an arbitrary constant c , we can by differentiation , and elimination ( if necessary ) of that con- stant , obtain the differential equation of the first order , of which the given equation ...
Página 12
... given abscissa of a result for y , x ' dæ2 ' given curve , i.e. of a curve determined as to its species by the form of its equation , and as to its elements by the values of the constants in that equation , correspond only definite ...
... given abscissa of a result for y , x ' dæ2 ' given curve , i.e. of a curve determined as to its species by the form of its equation , and as to its elements by the values of the constants in that equation , correspond only definite ...
Página 28
... equation given . 3. To illustrate the same doctrine geometrically , if x and y represent rectangular co - ordinates ... equation would be determined by a law , but an element of which , re- presented by a constant in that equation ...
... equation given . 3. To illustrate the same doctrine geometrically , if x and y represent rectangular co - ordinates ... equation would be determined by a law , but an element of which , re- presented by a constant in that equation ...
Otras ediciones - Ver todas
Términos y frases comunes
2ndly algebraic arbitrary constant arbitrary function assume C₁ C₂ Cambridge Chap Chapter College complete primitive condition Crown 8vo curve d²u deduce derived determined differential coefficients dp dq dp dy dv dv dx dx dx dy dx dz dx² dy dy dx dy dz dz dx dz dz Edition eliminating equa exact differential expressed Extra fcap fcap finite given equation Hence homogeneous functions Illustrations independent variable infinite integrating factor involving Mdx+Ndy method Mx+Ny obtained ordinary differential equations partial differential equation particular integral primitive equation Professor Prop reduced relation represent respect result satisfied second member second order Shew shewn singular solution substituting suppose theorem tion transformation V₁ V₂ whence X₁ Y₁ аф
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