Answers to selected odd-numbered problems begin on page ANS-2. dy dy 2ty(y – 1) dt + y? = ty dt 19. P 20. 3(1 + t²) an In Problems 21 and 22 solve the given initial-value problem. dy 2ху %3 Зу, у(1) %3D} 21. x dx dy + y3/2 = 1, y(0) = 4 dx 22. y/2 Each DE in Problems 23–30 is of the form given in (5). In Problems 23–28 solve the given differential equation by using an appropriate substitution. dy dy 24. dx 1 — х — у (x + y + 1)² 23. x + y dx dy dy 26. dx tan?(x + y) sin (x + y) 25. dx dy dy 28. dx 2 + Vy – 2x + 3 1 + ev-x+5 27. dx In Problems 29 and 30 solve the given initial-value problem. dy 29. dx cos (x + y), y(0) = 7/4 Зх + 2y dy 30. dx y(-1) = –1 Зх + 2у + 2" Discussion Problems 31. Explain why it is always possible to express any homogeneous differential equation M(x, y) dx + N(x, y) dy = 0 in the form dy F dx an х You might start by proving that М'x, у) %— х"М(1, у/x) N(x, y) = xªN(1, y/x). and 32. Put the homogeneous differential equation (5x2 — 2у?) dx — хуdy %3D 0 into the form given in Problem 31. copied, scanned, or duplicated, in whole or in part. WCN 02-200-202
Answers to selected odd-numbered problems begin on page ANS-2. dy dy 2ty(y – 1) dt + y? = ty dt 19. P 20. 3(1 + t²) an In Problems 21 and 22 solve the given initial-value problem. dy 2ху %3 Зу, у(1) %3D} 21. x dx dy + y3/2 = 1, y(0) = 4 dx 22. y/2 Each DE in Problems 23–30 is of the form given in (5). In Problems 23–28 solve the given differential equation by using an appropriate substitution. dy dy 24. dx 1 — х — у (x + y + 1)² 23. x + y dx dy dy 26. dx tan?(x + y) sin (x + y) 25. dx dy dy 28. dx 2 + Vy – 2x + 3 1 + ev-x+5 27. dx In Problems 29 and 30 solve the given initial-value problem. dy 29. dx cos (x + y), y(0) = 7/4 Зх + 2y dy 30. dx y(-1) = –1 Зх + 2у + 2" Discussion Problems 31. Explain why it is always possible to express any homogeneous differential equation M(x, y) dx + N(x, y) dy = 0 in the form dy F dx an х You might start by proving that М'x, у) %— х"М(1, у/x) N(x, y) = xªN(1, y/x). and 32. Put the homogeneous differential equation (5x2 — 2у?) dx — хуdy %3D 0 into the form given in Problem 31. copied, scanned, or duplicated, in whole or in part. WCN 02-200-202
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 15CR
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#31
Transcribed Image Text:Answers to selected odd-numbered problems begin on page ANS-2.
dy
dy
2ty(y – 1)
dt
+ y? = ty
dt
19. P
20. 3(1 + t²)
an
In Problems 21 and 22 solve the given initial-value problem.
dy
2ху %3 Зу, у(1) %3D}
21. x
dx
dy
+ y3/2 = 1, y(0) = 4
dx
22. y/2
Each DE in Problems 23–30 is of the form given in (5).
In Problems 23–28 solve the given differential equation by using an
appropriate substitution.
dy
dy
24.
dx
1 — х — у
(x + y + 1)²
23.
x + y
dx
dy
dy
26.
dx
tan?(x + y)
sin (x + y)
25.
dx
dy
dy
28.
dx
2 + Vy – 2x + 3
1 + ev-x+5
27.
dx
In Problems 29 and 30 solve the given initial-value problem.
dy
29.
dx
cos (x + y), y(0) = 7/4
Зх + 2y
dy
30.
dx
y(-1) = –1
Зх + 2у + 2"
Discussion Problems
31. Explain why it is always possible to express any homogeneous
differential equation M(x, y) dx + N(x, y) dy = 0 in the form
dy
F
dx
an
х
You might start by proving that
М'x, у) %— х"М(1, у/x)
N(x, y) = xªN(1, y/x).
and
32. Put the homogeneous differential equation
(5x2 — 2у?) dx — хуdy %3D 0
into the form given in Problem 31.
copied, scanned, or duplicated, in whole or in part. WCN 02-200-202
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