## A Treatise on Differential Equations, Volume 1 |

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2ndly admit algebraic arbitrary constants arbitrary function assumes the form axis becomes Chap Chapter complete primitive condition corresponding curvature deduce definite integrals degree dependent derived determined differential coefficients dx dx dx dy dy dy _ dy dx dy dz dz dz dz pdx eliminating envelope species equa equal equation given equation Mdx exact differential equation example expressed given equation gives Hence homogeneous equation homogeneous functions independent variable infinite integrating factor intrinsic equation inverse linear differential equation linear equation method multiplying obtained ordinary differential equations partial differential equation particular integral primitive equation problem Prop proposed equation reduced relation represent respect result satisfied second member second order Shew shewn singular integral singular solution solve substituting suppose symbolical form tangent Taylor's theorem theorem tion whence