Differential Equations of First Order and First Degree 2-9
18.
2
31
dydy
y
xx
dxdx
⎛⎞
−=+
⎜⎟
⎝⎠
.
Ans:
(
)
(
)
–331yxcx+=
19.
()
1cossin0
yy
exdxexdy++=.
Ans:
()
1sin
y
exc+=
20.
1
2
cos–20
y
yxxedy=
.
Ans:
1
sin+=
y
xec
21.
()
2
3cos1cot0
xx
eydxeydy++=
.
Ans:
()
3
tan1
x
yce=+
22.
(
)
cosxydydx+=.
Ans:
tan
2
xy
yc
+
⎛⎞
=+
⎜⎟
⎝⎠
23.
1
xy
dy
e
dx
+
+=.
Ans:
(
)
10
xy
xce
+
++=
24.
xyadyxya
xybdxxyb
⎛⎞⎛⎞
+−++
=
⎜⎟⎜⎟
+−++
⎝⎠⎝⎠
.
Ans:
(
)
(
)
(
)
2
1
log2
2
xy baxyabxc
⎡⎤
++−+−=+
⎣⎦
2.1.2 Homogeneous Equations
A polynomial f (x, y) is called a homogeneous function of degree n if
(,)(,)
n
ftxty tfxy=
for some tR∈ or equivalently,
(,)(1,).
n
fxyxfyx=
Example 2.1.10 (,)23fxy
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