## An Elementary Treatise on Differential Equations and Their Applications |

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approximation arbitrary constants arbitrary functions auxiliary equation axis c-discriminant Chap circle Clairaut's form complementary function complete integral complete primitive condition convergent cosh cusp-locus denote differential coefficients dx dy dz dy dx envelope Examples for solution EXAMPLES ON CHAPTER family of curves geometrical given giving Hence show holomorphic independent variables indicial equation infinite series integrating factor intermediate integral intersect Laplace's equation last article linear differential equation linear equation London method Miscellaneous Examples node-locus obtain occur ordinary differential equation orthogonal trajectories parabola partial differential equation particular integral particular solution plane positive integer prove putting regular integrals replaced respectively result Riccati's equation satisfied second order Similarly simultaneous equations singular integral singular points singular solution solve straight line subsidiary equations substitution surface tac-locus tangent theorem transformation values vanish Verify zero