A Treatise on Differential Equations, Volum 1Macmillan, 1872 - 85 sider |
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Resultat 1-5 av 83
Side xiv
... integral of the form u = f ( v ) , 362. Deduction of such integral when possible , 364. Relations of first integrals , 366. General rule , 369. Miscellaneous theorems . Poisson's method , 375 . Duality , 376. Legendre's Transformation ...
... integral of the form u = f ( v ) , 362. Deduction of such integral when possible , 364. Relations of first integrals , 366. General rule , 369. Miscellaneous theorems . Poisson's method , 375 . Duality , 376. Legendre's Transformation ...
Side 1
... Integral Calculus , on the other hand , it is the rela tion among the primitive variables , x , y , & c . which is sought . In that branch of the Integral Calculus with which the student B. D. E. Es 1 is supposed to be already familiar ...
... Integral Calculus , on the other hand , it is the rela tion among the primitive variables , x , y , & c . which is sought . In that branch of the Integral Calculus with which the student B. D. E. Es 1 is supposed to be already familiar ...
Side 13
... integrals . As the term primitive has reference to the direct processes of differentiation , & c . by which a differential equation is ... integral . It has been shewn that the order of succession in ART . 7. ] 13 SECOND AND HIGHER ORDERS .
... integrals . As the term primitive has reference to the direct processes of differentiation , & c . by which a differential equation is ... integral . It has been shewn that the order of succession in ART . 7. ] 13 SECOND AND HIGHER ORDERS .
Side 16
... integral . The second of the properties above noted constitutes a criterion by which it may be determined whether two dif- ferential equations of the first order , each involving an arbi- trary constant , originate from the same ...
... integral . The second of the properties above noted constitutes a criterion by which it may be determined whether two dif- ferential equations of the first order , each involving an arbi- trary constant , originate from the same ...
Side 17
... integral of the supposed equation of the second order . It is evident that ( 7 ) is the general type of all such first integrals . Thus the type of the first integrals of ( 3 ) would be y dy dy Φ x dx ' y2 - xy = dx = C. Ꮳ But any two ...
... integral of the supposed equation of the second order . It is evident that ( 7 ) is the general type of all such first integrals . Thus the type of the first integrals of ( 3 ) would be y dy dy Φ x dx ' y2 - xy = dx = C. Ꮳ But any two ...
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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