7. xy + y = x², x > 0 8.
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
Number 7 3.4 show all work

Transcribed Image Text:ph the solution to Example 5 by typing and ent
plot (exp (-x^2/2) *int (exp(t^2/2),t=0..x)+exp(-x^2/2),x=
This graph appears in Figure 3.8.
1.4E
1.2-
0.8 -
0.6-
0.4
0.2
2
3
Figure 3.8
vative
EXERCISES 3.4
dy
In Exercises 1–12, determine the integrating factor and
solve the differential equation.
1. y + y/x? = 0
11.
+e'y = e'
dt
dr
2. y' = y/x - 2, x > 0
12.
=r tan 0 + sin 0,0 < 0 < x/
de
3. y' – 2xy = x
4. y' = 4y +2x
In Exercises 13–18, solve the initial v
5. y = 1+
y
-, x >0
1+2x
13. y' +4y = 2, y(1) = 2
14. 2xy' + y = 1, y(4) = 0
y
2xy
6. y = x² .
1+x2
15. y + = 2, y(0) = 2
x+1
8. xy+y = x2, x < 0
16. y' + 2xy = 1, y(0) = –1
17. y' = cos 2x – y/x, y(1/2) = 0
7. xy + y = x², x > 0
9. (1+ xy) dx – x² dy = 0, x < 0
10. (1 + xy) dx – x² dy = 0, x > 0
18. x(x +1)y' 2 + y, y(1) = 0
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