## Differential Equations |

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algebraical factors assumed Auxiliary Equation c-discriminant Chapter Clairaut's equation cn yn commutative commutative operational constant coefficients corresponding Complementary Function degree dependent variable differential coefficient directly occurring discriminant relation double points Envelope Locus equa equation is reduced equation Mdx equation of order exact differential exact equation Examples for solution given differential equation given equation given system gives Hence independent arbitrary constants integrating factor inverse operator involving last equation left hand side linear differential equation linear equation linearly dependent method mutually independent arbitrary operational factors ordinary differential equation original equation orthogonal trajectories partial differential equation Particular Integral particular solution particular value rational integral equation rational integral function respect result right hand side roots seen side of equation singular solution solution of equation solvable Solve the differential substitution system f system of curves tangent term tion unique value