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Differential Equations by Pearson
book

Differential Equations by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
472 pages
13h 25m
English
Pearson India
Content preview from Differential Equations by Pearson
2-32 Diff erential Equations
2.1.4 Exact Equations
Defi nition 2.1.33 A differential equation which is obtained from
its primitive by mere differentiation without any further operation is
called an exact equation.
The equations
0, 0xd
y ydx xdx ydy+= +=
and
2
0
xdy ydx
x
=
are exact since these can be written as
1
22
2
()0, ( )0dxy dx y=+=
and
0,
y
d
x
⎛⎞
=
⎜⎟
⎝⎠
respectively.
The following theorem gives a criterion for exact equations.
Theor
em 2.1.34 If
(,)Mx
y
and
(,)Nxy
are real-valued func-
tions having continuous fi
rst partial derivati
ves on some rectangle
00
:,,Rx x ay y b−≤ −≤
then a necessary and suffi cient condition
for the equation
0Md
x Ndy+=
(2.48)
to be ...
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Publisher Resources

ISBN: 9781299487406Publisher Website