## A treatise on ordinary and partial differential equations |

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### Common terms and phrases

algebraic function arbitrary constant arbitrary function assumed axis becomes binomial equation Clairaut's equation coefﬁcients coeﬂicient complementary function complete integral condition constant of integration corresponding cosx deﬁned Denoting derived Determine the curve doubly inﬁnite system elimination equa equal roots equating to zero equation containing exact differential example expression ﬁnal ﬁnd ﬁnding ﬁrst degree ﬁrst integral ﬁrst member ﬁrst order ﬁrst term ﬁxed formula given differential equation given equation gives hence hypergeometric series independent integrals independent variable integral equation integral of equation integrating factor intersection inverse symbol l2mo let the given linear equation locus logx manner multiplied obtain operand orthogonal trajectories parabola partial differential equation particular integral powers preceding article reduced represents satisﬁed satisfy equation second degree second integral second member second order singular solution sinx surface system of curves t/ze tangent term containing tion transformation values vanish whence written