Formation of partial differential equations by eliminating arbitrary functions
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It consists primarily of how to form partial differential equations by eliminating arbitrary functions from a given relationship.
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Formation of partial differential equations by eliminating arbitrary functions
- 1. By Dr. B.M.B.Krushna Sr. Asst. Professor Dept. Of Mathematics MVGR COLLEGE OF ENGINEERING (A) Cluster-V Lecture 2 FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS (Formation of partial differential equations by eliminating arbitrary functions) 1
- 2. To form a partial differential equation by eliminating arbitrary functions from given relation Suppose the given relation contains one or more arbitrary functions then eliminating those arbitrary functions by differentiating the relation partially w.r.t. independent variables. Key points: If the number of arbitrary functions to be eliminated from given relation is one, we get first order type of a PDE. 2
- 3. If the number of arbitrary functions to be eliminated from given relation is two, one can get second order type of a PDE. The order of PDE is equal to the number of arbitrary functions which is obtained by the elimination of arbitrary functions from given relation. PDE corresponding to a relation is not unique. We may get one more partial differential equations corresponding to a relation but order of PDE is unique. 3
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- 6. Relationship between dependent variable, independent variables and arbitrary functions Relation Arbitrary function No. of Arbitrary functions PDE f 1 F(p, q, z, x, y)=0 f, g 2 F(r, s, t, p, q, z, x, y)=0 f 1 F(p, q, z, x, y)=0 f 1 F(p, q, z, x, y)=0 6
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- 10. Here the number of arbitrary functions is two, so we obtain second order PDE from this relation. 10
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