University of South Florida
Digital Commons @ University of
South Florida
Textbooks Collection Tampa Library
12-2013
Student Solutions Manual for Elementary Differential Equations
and Elementary Differential Equations with Boundary Value
Problems
William F. Trench
Trinity University,
Follow this and additional works at: https://digitalcommons.usf.edu/oa_textbooks
Part of the Mathematics Commons, and the Ordinary Differential Equations and Applied Dynamics
Commons
Recommended Citation
Trench, William F., "Student Solutions Manual for Elementary Differential Equations and Elementary
Differential Equations with Boundary Value Problems" (2013). Textbooks Collection. 7.
https://digitalcommons.usf.edu/oa_textbooks/7
This Book is brought to you for free and open access by the Tampa Library at Digital Commons @ University of
South Florida. It has been accepted for inclusion in Textbooks Collection by an authorized administrator of Digital
Commons @ University of South Florida. For more information, please contact .
, STUDENT SOLUTIONS MANUAL FOR
ELEMENTARY
DIFFERENTIAL EQUATIONS
AND
ELEMENTARY
DIFFERENTIAL EQUATIONS
WITH BOUNDARY VALUE
PROBLEMS
William F. Trench
Andrew G. Cowles Distinguished Professor Emeritus
Department of Mathematics
Trinity University
San Antonio, Texas, USA
This book has been judged to meet the evaluation criteria set by the Edi-
torial Board of the American Institute of Mathematics in connection with
the Institute’s Open Textbook Initiative. It may be copied, modified, re-
distributed, translated, and built upon subject to the Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported License.
,This book was published previously by Brooks/Cole Thomson Learning
Reproduction is permitted for any valid noncommercial educational, mathematical, or scientific purpose.
However, charges for profit beyond reasonable printing costs are prohibited.
, TO BEVERLY
Contents
Chapter 1 Introduction 1
1.2 First Order Equations 1
Chapter 2 First Order Equations 5
2.1 Linear First Order Equations 5
2.2 Separable Equations 8
2.3 Existence and Uniqueness of Solutions of Nonlinear Equations 11
2.4 Transformation of Nonlinear Equations into Separable Equations 13
2.5 Exact Equations 17
2.6 Integrating Factors 21
Chapter 3 Numerical Methods 25
3.1 Euler’s Method 25
3.2 The Improved Euler Method and Related Methods 29
Digital Commons @ University of
South Florida
Textbooks Collection Tampa Library
12-2013
Student Solutions Manual for Elementary Differential Equations
and Elementary Differential Equations with Boundary Value
Problems
William F. Trench
Trinity University,
Follow this and additional works at: https://digitalcommons.usf.edu/oa_textbooks
Part of the Mathematics Commons, and the Ordinary Differential Equations and Applied Dynamics
Commons
Recommended Citation
Trench, William F., "Student Solutions Manual for Elementary Differential Equations and Elementary
Differential Equations with Boundary Value Problems" (2013). Textbooks Collection. 7.
https://digitalcommons.usf.edu/oa_textbooks/7
This Book is brought to you for free and open access by the Tampa Library at Digital Commons @ University of
South Florida. It has been accepted for inclusion in Textbooks Collection by an authorized administrator of Digital
Commons @ University of South Florida. For more information, please contact .
, STUDENT SOLUTIONS MANUAL FOR
ELEMENTARY
DIFFERENTIAL EQUATIONS
AND
ELEMENTARY
DIFFERENTIAL EQUATIONS
WITH BOUNDARY VALUE
PROBLEMS
William F. Trench
Andrew G. Cowles Distinguished Professor Emeritus
Department of Mathematics
Trinity University
San Antonio, Texas, USA
This book has been judged to meet the evaluation criteria set by the Edi-
torial Board of the American Institute of Mathematics in connection with
the Institute’s Open Textbook Initiative. It may be copied, modified, re-
distributed, translated, and built upon subject to the Creative Commons
Attribution-NonCommercial-ShareAlike 3.0 Unported License.
,This book was published previously by Brooks/Cole Thomson Learning
Reproduction is permitted for any valid noncommercial educational, mathematical, or scientific purpose.
However, charges for profit beyond reasonable printing costs are prohibited.
, TO BEVERLY
Contents
Chapter 1 Introduction 1
1.2 First Order Equations 1
Chapter 2 First Order Equations 5
2.1 Linear First Order Equations 5
2.2 Separable Equations 8
2.3 Existence and Uniqueness of Solutions of Nonlinear Equations 11
2.4 Transformation of Nonlinear Equations into Separable Equations 13
2.5 Exact Equations 17
2.6 Integrating Factors 21
Chapter 3 Numerical Methods 25
3.1 Euler’s Method 25
3.2 The Improved Euler Method and Related Methods 29
