A Treatise on Differential Equations |
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2ndly algebraic arbitrary constants arbitrary function C₁ C₂ Chap Chapter complete primitive condition curve deduce derived determined differential coefficients dp dp dp dq dp dy dt dt dv du dv dv dv dx dx dx dy dz dx dz dx² dy dc dy dx dy dy dz dx dz dy dz dz Edition eliminating equa exact differential expressed Fcap finite given equation gives Hence homogeneous homogeneous functions independent variable infinite integrating factor involving linear equation method obtained ordinary differential equations partial differential equation particular integral pdx+qdy primitive equation problem Prop reduced relation represent respect result satisfied second member second order shew shewn singular solution substituting suppose theorem tion transformation whence X₁ y₁ аф
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