A treatise on differential equations, Volume 1

2ndly arbitrary constants arbitrary function C₁ C₂ Chap complete primitive condition corresponding curve d³y deduce derived determined differential coefficients dp dq dp dy dt dt dv du dv dv dv dx dx dx dy dz dx dz dx₁ dx² dy dx dz dx dz dy dz dz eliminating equa equal exact differential expressed finite given equation gives Hence homogeneous functions independent variable integrating factor linear equation Mdx+Ndy method Mx+Ny obtained ordinary differential equations partial differential equation particular integral primitive equation Prop proposed equation reduced relation represent respect result satisfied second member second order Shew shewn singular solution substituting suppose theorem tion transformation whence X₁ y₁ аф