A Treatise on Differential Equations, Том 1

2ndly arbitrary constant arbitrary function C₁ C₂ Chap complete primitive condition corresponding curve d³y deduce degree derived determined differential coefficients dp dq dp dy dv dv dv dx dx dx dy dy dx dz dx² dy dx dy dz dz dx dz dz eliminating envelope species equa equal exact differential expressed finite given equation gives Hence homogeneous functions independent variable infinite integrating factor involving linear equation Mdx+Ndy method multiplying Mx+Ny obtained ordinary differential equations partial differential equation particular integral primitive equation Prop reduced relation represent respect result satisfied second member second order Shew shewn singular solution substituting suppose symbolical form Taylor's theorem theorem tion transformation V₂ whence X₁ Y₁ аф