文档介绍：COMPLETE SOLUTIONS
MANUAL FOR
ZILL'S
A FIRST COURSE IN
DIFFERENTIAL
EQUATIONS
WITH MODELING APPLICATIONS
7TH EDITION
AND
ZILL & CULLEN'S
DIFFERENTIAL
EQUATIONS
WITH BOUNDARY·VALUE PROBLEMS
5TH EDITION
BROOKS/COLE
THOMSON LEARNING
Australia • Canada • Mexico • Singapore • Spain • United Kingdom • United States
Table of Contents
1 Introduction to Differential Equations 1
2 First-Order Differential Equations 22
3 Modeling with First-Order Differential Equations 71
4 Higher-Order Differential Equations 104
5 Modeling with Higher-Order Differential Equations 194
6 Series Solutions of Linear Equations 240
7 The Laplace Transform 308
8 Systems of Linear First-Order Differential Equations 370
9 Numerical Solutions of Ordinary Differential Equations 430
10 Plane Autonomous Systems and Stability 458
11 Orthogonal Functions and Fourier Series 491
12 Partial Differential Equations and Boundary-Value
Problems in Rectangular Coordinates 538
13 Boundary-Value Problems in Other Coordinate Systems 616
14 Integral Transform Method 654
15 Numerical Solutions of Partial Differential Equations 695
Appendix I Gamma function 717
Appendix II Introduction to Matrices 718
1 Introduction to Differential Equations
Exercises ---------------
1. Second-order; linear.
2. Third-order; nonlinear because of (dyjdx)4.
3. The differential equation is first-order. Writing it in thti form x(dyjdx) + y2 = 1, we see that it is
nonlinear in y because of y2 However, writing it in the form - 1) (dx j dy) + x = 0, we see that
it is linear in x.
4. differential equation is first-order. Writing it in the form u(dvjdu) + (1 + ueu we see
that it is linear in v. However, writing it in the form (v + uv ue11 )(d·ujdv) + u 0, we see that it
is nonlinear in u.
5. Fourth-order; linear
6. Second-order; nonlinear because of cos(r + u)
7. Second-order; nonlinear because of yl + (dyjdx