A Treatise on Differential Equations

2ndly arbitrary constant arbitrary function C₁ Chap Chapter complete primitive condition corresponding curve deduce degree derived determined differential coefficients dp dy dt dt dv dv dx dx dx dy dx dx dz dx² dy dx dy dy dy dy dz dz dx dz dz eliminating envelope species equa equal equation Mdx exact differential expressed finite given equation gives Hence homogeneous functions independent variable infinite integrating factor involving linear differential equation linear equation Mdx+Ndy method multiplying Mx+Ny obtained ordinary differential equations P₁ 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 whence y₁ аф