A Treatise on Differential EquationsMacmillan, 1865 - 496 σελίδες |
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Σελίδα viii
... determine the form of the Roots of Algebraic Equations , 1864 , pages 733 ... 755 . In the Transactions of the Royal Irish Academy . On the Analysis of Discontinuous Functions . Vol . 21 , 1848 , pages 124 ... 139 . On a certain ...
... determine the form of the Roots of Algebraic Equations , 1864 , pages 733 ... 755 . In the Transactions of the Royal Irish Academy . On the Analysis of Discontinuous Functions . Vol . 21 , 1848 , pages 124 ... 139 . On a certain ...
Σελίδα 1
... m + b ' = 0 . - The quantities A , A ' , C , C ' are determined by the system of equations A + A ' = a , Am1 + A'm2 = a ' , C + C ' = c , Çm , + C'm2 = c ' , B.D.E. II . from which we find am - a " стг C CHAPTER ADDITIONS TO CHAPTER.
... m + b ' = 0 . - The quantities A , A ' , C , C ' are determined by the system of equations A + A ' = a , Am1 + A'm2 = a ' , C + C ' = c , Çm , + C'm2 = c ' , B.D.E. II . from which we find am - a " стг C CHAPTER ADDITIONS TO CHAPTER.
Σελίδα 14
... determine c as a function of x , so leading to a singular solution ; nor , on the other hand , as an absolute constant , so leading to a particular primitive . Thus the particular primitive y = ecx being given , the condition dy dc ...
... determine c as a function of x , so leading to a singular solution ; nor , on the other hand , as an absolute constant , so leading to a particular primitive . Thus the particular primitive y = ecx being given , the condition dy dc ...
Σελίδα 17
... determine c as a continuous function of one of the vari- ables , the corresponding solution of the differential equation is singular , and is geometrically represented by an envelope of the curves of primitives . But it may be , as we ...
... determine c as a continuous function of one of the vari- ables , the corresponding solution of the differential equation is singular , and is geometrically represented by an envelope of the curves of primitives . But it may be , as we ...
Σελίδα 18
... determines c as a function of x , and leads to the second of the solutions obtained above . The first , though it does not determine c as a function of x , still ex- presses a relation between c and x , which is the ground of the ...
... determines c as a function of x , and leads to the second of the solutions obtained above . The first , though it does not determine c as a function of x , still ex- presses a relation between c and x , which is the ground of the ...
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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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