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Mathematical Methods by Pearson
book

Mathematical Methods by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
437 pages
17h 41m
English
Pearson India
Content preview from Mathematical Methods by Pearson
12-18 Mathematical Methods
so that we have dz = a dx + f (a) dy.
Integrating, we get the complete integral as
() or ()zax fadyc zaxfayc=+ + =+ +
(12.66)
where a and c are arbitrary constants.
Note 1 We can put q = a instead of p = a and proceed
to obtain the complete integral.
Example 12.41
Solve pq = k
Solution The complete integral is
k
zax yc
a
=+ +
(1)
where a and
c are arbitrary constants
The general integral is obtained by eliminating
a between the equations
1
()
k
zax y a
a
f=+ + (2)
where c has been replaced by f ( a) and
2
0()
k
xya
a
f=− +
(3)
obtained by differentiating with respect to a.
The singular integral, if it exists, is determined
from the ...
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Publisher Resources

ISBN: 9781299446557Publisher Website