Differential Equations of First Order and First Degree 2-49
Example 2.1.52 Solve
()0.xydxdy−−=
Solution
,1,
1,0;
10
1()
1
MN
yx
MxyN
MN
yx
px
N
∂∂
∂∂
=−=−
∂∂
=−=
∂∂
−
−−
===
−
(Constant can be considered as a function of x.)
By Rule 3, the
()1
integrating factoris.
pxdxdxx
eee
∫∫
==
Multiplying by the integrating factor
,
x
e=
the equation can be
written as
()(1)
xxxxx
xedxyedxedyxeyec=+⇒−=+
or 1.
x
xyce
−
=++
Example 2.1.53 Solve
22
(32)(2)0.xyydxxxydy−+−=
Solution
22
32,2
34,22
MxyyNxxy
MN
xyxy
yx
MN
yx
=−=−
∂∂
=−=−
∂∂
∂∂
≠
∂∂
(34)(22)
(2)
21
(), afunction of
(2)
MN
yx
xyxy
Nxxy
xy
pxx
xxyx
∂∂
∂∂
−
−−−
=
−
−
===
−
By Rule 3, the
1
()log
integrating factor ...
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