A Treatise on Differential Equations

2ndly arbitrary constants arbitrary function assume C₁ Chap Chapter complete primitive condition Crelle's Journal curve deduce derived determined dF dF differential coefficients dp dp dp dq dp dx dp dy dv du dv dv dv dx dp dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dz eliminating ential equation equa equation dy exact differential expression finite given equation Hence homogeneous functions independent variables infinite integrating factor involving method multiplying obtained ordinary differential equations P₁ partial differential equation particular integral primitive equation reduced relation represent respect result satisfied second member second order shew shewn singular solution substituting suppose symbolical theorem theory tion transformation u₁ vanish whence X₁ y₁ аф