## A Treatise on Ordinary and Partial Differential Equations |

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### Common terms and phrases

_ dz arbitrary constant arbitrary function assumed ax2 ax axis becomes Besselian binomial equation characteristic Clairaut's equation complementary function complete integral constant of integration corresponding Denoting Determine the curve doubly infinite system dx dy dz dx2 dx elimination equa equal roots equation containing exact differential example expression formula given differential equation given equation given in Art Hence homogeneous homogeneous function hypergeometric series independent integrals independent variable integral equation integral of equation integrating factor intersection inverse symbol involving Legendre's equation let the given linear equation locus manner multiplied obtain operand ordinary differential equations orthogonal trajectories parameter partial differential equation particular integral plane preceding article reduced relation respect satisfies equation second degree second integral second member second order singly infinite system singular solution Solve the following system of curves tangent term containing tion transformation vanish whence written