A Treatise on Differential EquationsMacmillan, 1865 - 496 páginas |
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Página 1
... constructed from ) , an equation in which the variables are separated . Assume as this equation and let ( Ay ' + C ' ) dx ' + ( A'x ' + C ' ) dy ' = 0 ............... . ( 1 ) x ' = x + m2y , y ' = = x + m2y • It will be seen that in ...
... constructed from ) , an equation in which the variables are separated . Assume as this equation and let ( Ay ' + C ' ) dx ' + ( A'x ' + C ' ) dy ' = 0 ............... . ( 1 ) x ' = x + m2y , y ' = = x + m2y • It will be seen that in ...
Página 20
... construct in a developed form the complete primitive . See Chap . II . Art . 12 . The values of dy , day , & c . ad ... constructed so as to yield the same value of dp = ∞ is only dy dy as the given dx differential equation does . If it ...
... construct in a developed form the complete primitive . See Chap . II . Art . 12 . The values of dy , day , & c . ad ... constructed so as to yield the same value of dp = ∞ is only dy dy as the given dx differential equation does . If it ...
Página 54
... construct a differential equa- tion for determining dy , and , solving it , form the expression for y + dy , and from the number of infinitesimal arbitrary constants it contains , determine the nature of that general value of y of which ...
... construct a differential equa- tion for determining dy , and , solving it , form the expression for y + dy , and from the number of infinitesimal arbitrary constants it contains , determine the nature of that general value of y of which ...
Página 60
... constructing the system of ordinary differential equations ( 3 ) , deducing their general integrals u = α , v = b , and then constructing from these the primitive ( 1 ) . But the question arises , Will this be the most general solu ...
... constructing the system of ordinary differential equations ( 3 ) , deducing their general integrals u = α , v = b , and then constructing from these the primitive ( 1 ) . But the question arises , Will this be the most general solu ...
Página 61
... construct the equation F ( u , v ) = 0 . This will be the general solution sought . [ Art . 3 was intended to follow Chap . XIV . Art . 5. ] 3. The above theory may be extended to linear partial dif- ferential equations of the first ...
... construct the equation F ( u , v ) = 0 . This will be the general solution sought . [ Art . 3 was intended to follow Chap . XIV . Art . 5. ] 3. The above theory may be extended to linear partial dif- ferential equations of the first ...
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Términos y frases comunes
arbitrary constants Cambridge Chap Chapter College complete primitive condition Crelle's Journal Crown 8vo deduce derived determine dF dF dF dF dF dF dp dF dx dFdF differential coefficients dp dF dp dp dx dp dq dp dy dp₁ dq dp dv dv dx dp dp dx dx dx dy dy dx dz dx₁ dx² dy dp dy dx dy dz dz dy dz dz Edition eliminate equa Eton College expression Extra fcap factor function given equation Hence J. P. MAHAFFY Jacobi Last Multiplier linear partial differential m₁ memoir ordinary differential equations Owens College P₁ partial differential equations particular integral Professor Boole reduced represent result revised School shewn singular solution system of ordinary theorem theory tion transformation u₁ u₂ values vanish whence X₁ Y₁ аф
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