A Treatise on Differential Equations |
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Page 3
... equal to ê . Hence the solution becomes du dk = C. In applying this theory to the reduction of the general solution ( 2 ) in the case in which m1 = m2 , it must be observed that the numerator of the first member is the same function of ...
... equal to ê . Hence the solution becomes du dk = C. In applying this theory to the reduction of the general solution ( 2 ) in the case in which m1 = m2 , it must be observed that the numerator of the first member is the same function of ...
Page 6
... equal portions , to each of which the general theorem of solution may be applied . If x - x , be very small the theorem may be approximately represented by Хо y — y 。= f ( x 。, y . ) ( x − x . ) . On these principles Cauchy has ...
... equal portions , to each of which the general theorem of solution may be applied . If x - x , be very small the theorem may be approximately represented by Хо y — y 。= f ( x 。, y . ) ( x − x . ) . On these principles Cauchy has ...
Page 14
... equal quantities . [ See Chap . VIII . Art . 8. ] It would not there- fore be infinite . Hence we conclude that would not become dp dy infinite for a particular primitive in the strict sense of that term , i . e . for a solution derived ...
... equal quantities . [ See Chap . VIII . Art . 8. ] It would not there- fore be infinite . Hence we conclude that would not become dp dy infinite for a particular primitive in the strict sense of that term , i . e . for a solution derived ...
Page 30
... equal to f ( x , u ) , or to ƒ ( x , u ) deprived of any factor which neither vanishes nor becomes infinite when u = = 0. If that integral tend to 0 with u the solution is singular . Ex . 1. Determine whether y = 0 is a singular ...
... equal to f ( x , u ) , or to ƒ ( x , u ) deprived of any factor which neither vanishes nor becomes infinite when u = = 0. If that integral tend to 0 with u the solution is singular . Ex . 1. Determine whether y = 0 is a singular ...
Page 31
... equal to 0. But the course of the demonstra- tion shews that the value of the definite integral must be first obtained on the hypothesis that u ( in this case replaced by y ) is finite , and then the limiting value which its expression ...
... equal to 0. But the course of the demonstra- tion shews that the value of the definite integral must be first obtained on the hypothesis that u ( in this case replaced by y ) is finite , and then the limiting value which its expression ...
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Common terms and phrases
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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