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Complete Solutions Manual A First Course in Differential Equations with Modeling Applications Ninth Edition
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Complete Solutions Manual A First Course in Differential Equations with Modeling Applications Ninth Edition (Complete Guide)

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Complete Solutions Manual

A First Course in Differential Equations
with Modeling Applications
Ninth Edition

Dennis G. Zill
Loyola Marymount University


Differential Equations with
Boundary-Vary Problems
Seventh Edition

Dennis G. Zill
Loyola Marymount University

Michael R. Cullen
Late of Loyola Marymount University




By

Warren S. Wright
Loyola Marymount University

Carol D. Wright



* ; BROOKS/COLE
C E N G A G E Learning-


Australia • Brazil - Japan - Korea • Mexico • Singapore • Spain • United Kingdom • United States

, Table of Contents
1 Introduction to Differential Equations 1

2 First-Order Differential Equations 27

3 Modeling with First-Order Differential Equations 86

4 Higher-Order Differential Equations 137

5 Modeling with Higher-Order Differential Equations 231

6 Series Solutions of Linear Equations 274

7 The Laplace Transform 352

8 Systems of Linear First-Order Differential Equations 419

9 Numerical Solutions of Ordinary Differential Equations 478

10 Plane Autonomous Systems 506

11 Fourier Series 538

12 Boundary-Value Problems in Rectangular Coordinates 586

13 Boundary-Value Problems in Other Coordinate Systems 675

14 Integral Transforms 717

15 Numerical Solutions of Partial Differential Equations 761
Appendix I Gamma function 783
A ppendix II Matrices 785

,3.ROOKS/COLE
C 'N G A G E L e a rn in g ”




i 2009 Brooks/Cole, Cengage Learning ISBN-13. 978-0-495-38609-4
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:"tcd in Canada
1 3 4 5 6 7 11 10 09 08

, 1 Introduction to Differential Equations


1 . Second order; linear

2 . Third order; nonlinear because of (dy/dx)4

3. Fourth order; linear

4. Second order; nonlinear bccausc of cos(r + u)

5. Second order; nonlinear because of (dy/dx)2 or 1 + (dy/dx)2

6 . Second order: nonlinear bccausc of R~

7. Third order: linear

8 . Second order; nonlinear because of x2

9. Writing the differential equation in the form x(dy/dx) -f y2 = 1. we sec that it is nonlinear in y
because of y2. However, writing it in the form (y2 —1)(dx/dy) + x = 0, we see that it is linear in x.

10. Writing the differential equation in the form u(dv/du) + (1 + u)v = ueu wc see that it is linear in
v. However, writing it in the form (v + uv —ueu)(du/dv) + u — 0, we see that it, is nonlinear in ■
Ji­

ll. From y = e-*/2 we obtain y' = —\e~x'2. Then 2y' + y = —e~X//2 + e-x/2 = 0.

12 . From y = | — |e-20* we obtain dy/dt = 24e-20t, so that


% + 20y = 24e~m + 20 - |e_20t) = 24.
clt \'o 5 /

13. R'om y = eix cos 2x we obtain y1= 3e^x cos 2x — 2e3* sin 2a? and y” = 5e3,xcos 2x — 12e3,xsin 2x, so
that y" — (k/ + l?>y = 0.

14. From y = —cos:r ln(sec;r + tanrc) we obtain y’ — —1 + sin.Tln(secx + tana:) and
y" = tan x + cos x ln(sec x + tan a?). Then y" -f y = tan x.

15. The domain of the function, found by solving x + 2 > 0, is [—2, oo). From y’ = 1 + 2(x + 2)_1/2 we


1

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