Литвин І.І., Конопчук О.М., Желізняк Г.О. Вища математика
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181
9.5. &.
1. R < (?
2. W ( ( ?
3. 5! ( :
) &
cc
+ 2&
c
= 0;') &
c
– &tgx =
x
cos
1
;
) &
cc
+ &
ccc
= &c;) &&
c
+
2
– 2& = 0.
4. R ( ’ < ( ?
5. R ’ ( < ?
6. R ’ ( < !?
7. R (! ) (!) 9?
8. /, ! ’ ( &
c
ctgx + & = 2 <
& = cosx.
9. C9 ( ( ()
.
10. R ’) ( () ?
11. C9 ( ( 9 (.
12. R ’< ( 9 (?
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( ( <?
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<, 7 ! :
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3
1
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. C ,,
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17. / ! (
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I’ ( ( ! ’, 7 (-
< (( :
18.
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c
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, y(0) = 1.
19.
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3
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1
(
23
c
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x
y
x
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20.
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1
1
2
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c
x
y
y
0)
4
(
S
y
.
9. [6*$ "
182
21.
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2
2
c
y
exyy
,
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.
22.
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x
c
,
1)0( y
.
23.
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c
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,
1)
4
(
S
y
.
24.
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5
(
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5
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2
3
3
2
dy=0,
y
x
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y
x
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.
25.
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22
dxxydxyx
0)3( y
.
26.
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22
dyxyxydx
0)8( y
.
27.
5
yy
c
,
25)0( y
.
28. 0lntg xdyxydx ,
ey
¸
¹
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2
S
.
29. &
c
= 2
2
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6
1
.
30. &
c
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2
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31.
,011
22
dyxdxy
32.
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22
dyxdxy
&(1) = 2.
33. &
c
+2& =
-2
, &(0) = 0.
34. &
c
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2
-4
, &(0) =
35.
2
&
c
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2
1
) = 62.
36. &
c
+& = cosx ,
37.
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2
xxy
dx
dy
38.
,1 xy
dx
dy
39.
,
2
xxy
dx
dy
9. [6*$ "
183
40.
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2
xy
dx
dy
41.
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2
xyy
42.
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2
xxxxyy
43.
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dx
dy
44.
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dx
dy
xx
45. ,01
cc
y 0)0(,2)0(
c
yy .
46. ,032
c
cc
yyy 0)0(,8)0(
c
yy .
47. ,02510
c
cc
yyy 8)0(,2)0(
c
yy .
48.
,096
c
cc
yyy
2)0(,1)0(
c
yy .
49. ,082
c
cc
yyy 4)0(,4)0(
c
yy .
50. ,020
c
cc
yyy
0)0(,
5
9
)0(
c
yy
.
51.
,06
c
cc
SSS
0)0(,5)0(
c
SS .
52. ,022
c
cc
yyy 0)0(,3)0(
c
yy .
53. ,0136
c
cc
yyy 11)0(,3)0(
c
yy .
54. ,0134
c
cc
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c
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184
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u
c
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u=u(x)+C.
5. C
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y=(u(x)+C)v(x).
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