It consists primarily of how to form partial differential equations by eliminating arbitrary functions from a given relationship.

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)
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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.
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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.
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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
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10. Here the number of arbitrary functions is two, so we obtain second order
PDE from this relation.
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