A Treatise on Differential Equations: Supplementary Volume

admit appear application arbitrary constants assume auxiliary becomes Chap Chapter combination common complete primitive condition connecting consider consist construct contain corresponding deduce depend derived determine developed dF dF dF differential coefficients dP dP dx dy dy dy dy dz dz dz eliminate envelope equa equal equivalent established expression factor final function give given equation Hence identically idul important infinite integral involving known lead linear partial differential memoir method multiplied necessary obtain ordinary differential equations original partial differential equation particular possible present Professor proposed proposition quantities reduced relation remains remarkable represent respect result roots satisfied shewn simultaneous singular solution substituting suppose surface theorem theory tion transformation values vanish variables whence