A Treatise on Differential Equations

2ndly algebraic arbitrary constant arbitrary function C₁ C₂ Cambridge Chap cloth College complete primitive condition corresponding Crown 8vo curve deduce degree derived determined dF do dF differential coefficients dp dy dt dt dx dx dx dy dx dx dz dx² dy dy dy dz dz dx dz dz eliminating envelope species equa exact differential example expression Fcap finite given equation gives Hence homogeneous functions independent variable infinite integrating factor involving linear equation Mdx+Ndy method Mx+Ny obtained ordinary differential equations P₁ partial differential equation particular integral primitive equation reduced relation represent respect result satisfied second member second order shew singular solution substituting supposed symbolical form theorem tion transformation V₂ whence X₁ Y₁ аф