First order partial differential equations

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

1. By
Dr. B.M.B.Krushna
Sr. Asst. Professor
Dept. Of Mathematics
MVGR COLLEGE OF ENGINEERING (A)
1

FIRST ORDER PARTIAL DIFFERENTIAL
EQUATIONS

2. A partial differential equation(shortly., PDE) is
an equation for a function which depends on
more than one independent variable which
involves the independent variables, the
function, and partial derivatives of the
function.

3. 

4. The order of a PDE is defined as the order of
the highest order derivative occur in the
equation.

The degree of a PDE is defined as the +ve
integral power to which the highest order
derivative occur in the equation.

5. 

6. We can form a PDE in Two ways

Elimination of arbitrary constants from a
relation f(x,y,z,a,b,…)=0


Elimination of arbitrary functions

7. General rules to remember.
If the number of arbitrary constants to be
eliminated is equal to the number of
independent variables, then we get a PDE
of first order.
If the number of arbitrary constants to be
eliminated is greater than the number of
independent variables, then we get a PDE
of 2
nd
or higher order. In this case we may
get more than one PDE.

8. If the number of arbitrary constants to be
eliminated is less than the number of
independent variables, then we get a PDE of
first order.
In this case we may get more than one PDE.

Note. In this chapter we use z=f(x,y), where x,y
are independent variables and z is dependent
variable.

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