Reproduce the given computer-generated direction field. Then sketch an approximate solution curve that passes through each of the indicated points. -= x² - y² dy dx (a) y(-2) = 1 (a) 3 0 3 (b) y(3) = 0 1 2 0 1 0 (c) y(0) = 2 0 3 1 0 -1 Y(u) = U 3 0 1 AA. M 0 -3 -3 -2 1 AAA www w 444 AAA AAAAA AA. - 3 xxxxx - 3 -2 -1 -2 A 44 xxxxx Y -2 ✓Y AAAA2 AAAA AAA44 ✓ ✓ AAA: - 3 -2 -1 -1 AAAAA2 xxxx y y 0 y YY www▼Y Y Y Y Y Y YYYY YYY 0 y YYYYY 0 y Y YYY y y -3 -2 -1 0 1 1 y 1 1 YY VIY Y Y Y YYYYY Y Y YYYYY 2 3 0 1 2 2 2 2 3 1 2 wwxx 1 2 3 3 3 3 3 X - 3 -2 -1 0 1 2 3 X 1 0 2 1 0 2 1 0 -1 3 2 1 0 3 21 1 0 -1 -3 A A A A -3 -2 -3 -2 AAAA444 AAAAA2 -3 -2 ✓✓ ***Y YY A A AAAA AAAA M ^^^^4 AA ^^ - 3 AAA V A44 ^^ AAAAA 1 -1 -2 -1 y y y Y YYYYYY 0 y 0 0 YY xxxx YY YY YY YYYY y 0 y 1 2 1 1 Y IY YYYYY 1 1 Y YYYY 2 2 2 3 1 2 3 -3 -2 -1 0 1 2 3 2 3 3 1 MIX AAA -1 -3 -2 -1 0 1 2 3 3 3 3 X X X X X
Reproduce the given computer-generated direction field. Then sketch an approximate solution curve that passes through each of the indicated points. -= x² - y² dy dx (a) y(-2) = 1 (a) 3 0 3 (b) y(3) = 0 1 2 0 1 0 (c) y(0) = 2 0 3 1 0 -1 Y(u) = U 3 0 1 AA. M 0 -3 -3 -2 1 AAA www w 444 AAA AAAAA AA. - 3 xxxxx - 3 -2 -1 -2 A 44 xxxxx Y -2 ✓Y AAAA2 AAAA AAA44 ✓ ✓ AAA: - 3 -2 -1 -1 AAAAA2 xxxx y y 0 y YY www▼Y Y Y Y Y Y YYYY YYY 0 y YYYYY 0 y Y YYY y y -3 -2 -1 0 1 1 y 1 1 YY VIY Y Y Y YYYYY Y Y YYYYY 2 3 0 1 2 2 2 2 3 1 2 wwxx 1 2 3 3 3 3 3 X - 3 -2 -1 0 1 2 3 X 1 0 2 1 0 2 1 0 -1 3 2 1 0 3 21 1 0 -1 -3 A A A A -3 -2 -3 -2 AAAA444 AAAAA2 -3 -2 ✓✓ ***Y YY A A AAAA AAAA M ^^^^4 AA ^^ - 3 AAA V A44 ^^ AAAAA 1 -1 -2 -1 y y y Y YYYYYY 0 y 0 0 YY xxxx YY YY YY YYYY y 0 y 1 2 1 1 Y IY YYYYY 1 1 Y YYYY 2 2 2 3 1 2 3 -3 -2 -1 0 1 2 3 2 3 3 1 MIX AAA -1 -3 -2 -1 0 1 2 3 3 3 3 X X X X X
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
4-1
Transcribed Image Text:Reproduce the given computer-generated direction field. Then sketch an approximate solution curve that passes through each of the indicated points.
-= x² - y²
dy
dx
(a) y(-2) = 1
(a)
3
0
3
(b) y(3) = 0
1
2
0
1
0
(c) y(0) = 2
0
3
1
0
-1
Y(u) = U
3
0
1
AA.
M
0
-3
-3 -2
1 AAA
www
w
444
AAA
AAAAA
AA.
- 3
xxxxx
- 3 -2 -1
-2
A 44
xxxxx
Y
-2
✓Y
AAAA2
AAAA
AAA44
✓ ✓
AAA:
- 3 -2 -1
-1
AAAAA2
xxxx
y
y
0
y
YY
www▼Y Y Y Y Y Y
YYYY
YYY
0
y
YYYYY
0
y
Y YYY
y
y
-3 -2 -1 0
1
1
y
1
1
YY
VIY Y Y
Y YYYYY
Y Y
YYYYY
2 3
0 1 2
2
2
2 3
1 2
wwxx
1 2
3
3
3
3
3
X
- 3 -2 -1 0 1 2 3
X
1
0
2
1
0
2
1
0
-1
3
2
1
0
3
21
1
0
-1
-3
A A A
A
-3 -2
-3 -2
AAAA444
AAAAA2
-3 -2
✓✓
***Y YY
A A
AAAA
AAAA
M
^^^^4
AA
^^
- 3
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V
A44
^^
AAAAA
1
-1
-2 -1
y
y
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YYYYYY
0
y
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xxxx YY
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y
0
y
1 2
1
1
Y IY
YYYYY
1
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2
2
2 3
1 2
3
-3 -2 -1 0 1 2
3
2 3
3
1
MIX
AAA
-1
-3 -2 -1 0 1 2
3
3
3
3
X
X
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X
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