## A Treatise on Differential Equations |

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### Common terms and phrases

arbitrary constants arbitrary function assumed 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 dy _ dz elimination equa equal roots equation containing exact differential example expression finite formula given differential equation given equation given in Art gives Hence homogeneous functions 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 moving point multiplied obtain operand ordinary differential equations orthogonal trajectories parameter partial differential equation particular integral preceding article primitive putting reduced relation result satisfies equation satisfies the equation second degree second integral second member second order singular solution Solve the following substituting system of curves tangent tion transformation vanish whence written