A Treatise on Differential Equations

2ndly arbitrary constant arbitrary function C₁ C₂ Chap Chapter complete primitive condition corresponding curve d²u d³y deduce degree derived determined differential coefficients dp dq dp dy dv dv dv dx dx dx dy dy dx dz dx² dy 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 P₁ 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 symbolical form theorem tion transformation V₁ whence X₁ Y₁