A Treatise on Differential Equations

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