Complete Solutions Manual A First Course in Differential Equations with Modeling Applications Ninth Edition Dennis G. Zill
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Differential Equations with Modeling Applications
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Differential Equations With Modeling Applications
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A First Course in Differential Equations with Modeling Applications
The domain of the function, found by solving x +2 > 0, is [—2, oo). From y’ = 1+ 2(x + 2)_1/2 we
1Exercises 1.1 Definitions and Terminology
have
{y - x)y' = (y - ®)[i + (20 + 2)_1/2]
= y — x + 2(y - x)(x + 2)-1/2
= y - x + 2[x + 4(z + 2)1/2 - a;] (a: + 2)_1/2
= y — x + 8(ac + 2)1;...
a first course in differential equations with mode
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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
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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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