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admit appear application arbitrary constants assume auxiliary becomes Boole changing Chap Chapter co-ordinates combination common complete primitive condition connecting consider consists construct contain corresponding deduce demonstration depend derived determine developed dF dF differential coefficients eliminate envelope equa equal equivalent established expression factor final function give given equation Hence identically important independent variables infinite integral involving known lead linear partial differential manuscript memoir method multiplied necessary noticed obtain ordinary differential equations original partial differential equation particular possible present Professor PROP proposed proposition quantities question reduced regarding relation remains remarkable represent respect result roots satisfied shewn simultaneous single singular solution substituting sufficient suppose surface symbol theorem theory tion transformation values vanish vari variables whence
الصفحة viii - On Simultaneous Differential Equations of the First Order in which the Number of the Variables exceeds by more than one the Number of the Equations, 1862, pages 437. ..454. On the Differential 'Equations of Dynamics. A sequel to a Paper on Simultaneous Differential Equations, 1863, pages 485.
الصفحة 146 - ... second degree ; 2ndly that this system may be resolved into four systems, each consisting of two partial differential equations of the first order and first degree, two of which systems are irrelevant and the other two relevant ; Srdly that the solution of the two relevant systems ultimately depends on the solution of a system of ordinary differential equations of the first order, and that from these ordinary differential equations the given equation of the second order may be deduced independently...