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Equations of the First Order and of Degree Higher than the First Article Page 1 Introduction
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arbitrary function assumed auxiliary equation c-discriminant relation Clairaut's equation commutative operational Complementary Function complete solution constant coefficients dependent variable double points dx dx Envelope Locus equa equation is reduced equation of order equation Pdx exact differential Examples for solution Form the differential formula given differential equation given equation given system gives Hence independent arbitrary constants infinite system integrating factor inverse operator last equation left hand side linear differential equation linear equation mutually independent arbitrary operational factors ordinary differential equation orthogonal trajectories parabolas partial differential equation particular integral particular solution particular value proved as follows rational integral equation rational integral function respect result right hand side roots satisfies the differential seen singular solution solution of equation solvable Solve the differential substitution system f system of curves tangent tion