19. x' = -2y, y' = 2x; x(0) = 1, y(0) = 0 %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Need help for #19 and 24
Transcribed Image Text:4.1 Problems
In Problems 1 through 16, transform the given differential
equation or system into an equivalent system of first-order dif-
ferential equations.
3. x" + 2x' + 26x = 82 cos 4t (This equation was used in
Section 3.6 to model the oscillations of a mass-and-spring
system.)
4. x(3) – 2x"+x' = 1+te
1. х" + 3x' + 7х — 12
5. x(4) + 3x" + x = e' sin 2t
6. x(4) + 6x" – 3x' + x = cos 3t
7. 12x" +tx' + (t² – 1)x = 0
2. х" + 4х —х3
= 0 (This equation is used in Section 6.4
to describe the motion of a mass connected to a "soft"
spring.)
Transcribed Image Text:Use the method of Examples 6, 7, and 8 to find general solu-
tions of the systems in Problems 17 through 26. If initial con-
ditions are given, find the corresponding particular solution.
For each problem, use a computer system or graphing calcu-
lator to construct a direction field and typical solution curves
for the given system.
17. х' — у, у 3D —х
18. х' — у, у — х
19. х' %3D —2у, у'
20. х' 3D 10у, у' %3D — 10х; x(0) %3 3, у (0) — 4
21. x' = y, y' = -8x
22. x' = 8y, y' = -2x
23. x %3D у, у' %3 6х — у; x (0) —D 1, у (0) —D 2
%3D — у, у' %3 10х — 7у; x(0) %3D2, у (0) %3D —7
25. х %3D— у, у' %3D13х + 4y; x(0) %3D 0, у (0) — 3
26. х — у, у' %3D — 9х + бу
= 2x; x (0) = 1, y(0) = 0
1, у (0) 3D 0
%3D
24. x'
= -
0, у (0) 3D 3
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