A Treatise on Differential Equations, Volum 1Macmillan, 1872 - 85 sider |
Inni boken
Resultat 1-5 av 90
Side xiv
... Condition of derivation from a single primitive , 275. Solution , 276. General rule and ex- amples , 279. Homogeneous equations , 281. Integrating fac- tors , 282. Equations not derivable from a single primitive , 283 . More than three ...
... Condition of derivation from a single primitive , 275. Solution , 276. General rule and ex- amples , 279. Homogeneous equations , 281. Integrating fac- tors , 282. Equations not derivable from a single primitive , 283 . More than three ...
Side 4
... condition , already referred to , that one at least of the differential coefficients must explicitly present itself . All the above equations may at once be referred to the typical form by transposition of their second member , 3 ...
... condition , already referred to , that one at least of the differential coefficients must explicitly present itself . All the above equations may at once be referred to the typical form by transposition of their second member , 3 ...
Side 23
... shall first establish a prelimi- nary proposition expressing the condition of mutual depend- ence of functions of two variables ; I shall then ( 23 ) CHAPTER II ON DIFFERENTIAL EQUATIONS OF THE FIRST ORDER AND DEGREE BETWEEN TWO VARIABLES •
... shall first establish a prelimi- nary proposition expressing the condition of mutual depend- ence of functions of two variables ; I shall then ( 23 ) CHAPTER II ON DIFFERENTIAL EQUATIONS OF THE FIRST ORDER AND DEGREE BETWEEN TWO VARIABLES •
Side 24
... condition dV dv dV dv dx dy dy dx = 0 ........ ( 1 ) will be identically satisfied . Conversely , if this condition be identically satisfied , V will be expressible as a function of v . 1st . For suppose V = ( v ) . Then dV_dp ( v ) dv ...
... condition dV dv dV dv dx dy dy dx = 0 ........ ( 1 ) will be identically satisfied . Conversely , if this condition be identically satisfied , V will be expressible as a function of v . 1st . For suppose V = ( v ) . Then dV_dp ( v ) dv ...
Side 25
... condition of the functional dependence of V and v . For suppose either V or v , and for distinction we shall choose v , to be a function of one of the variables only , as x ; and V to be a function of v . Then is also a function of x ...
... condition of the functional dependence of V and v . For suppose either V or v , and for distinction we shall choose v , to be a function of one of the variables only , as x ; and V to be a function of v . Then is also a function of x ...
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A Treatise on Differential Equations: Supplementary Volume George Boole Uten tilgangsbegrensning - 1865 |
Vanlige uttrykk og setninger
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