Solution Manual for

Ordinary Differential Equations

An Introduction to the Fundamentals

(First Edition, 2016)

  Published by CRC Press


Prepared by Dr. Kenneth Howell,

Department of Mathematical Sciences, University of Alabama in Huntsville


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Below are the chapters of the solution manual for Ordinary Differential Equations: An Introduction to the Fundamentals, published by CRC Press.  (More precisely, below are the links to pdf files for the chapters.)



Some General Comments and Warnings:


1)  These solutions should be used only as a last resort!  Try doing the work yourself, first, using what is in the text as a guide.  If you need help, then see your instructor or go to any math tutoring service available to you.  Only if all else fails should you peek at the solutions here.


2)  Keep in mind that there may be several ways to answer a single problem.  What is given here is only one possible way to derive each correct answer.


3)  Beware of tpyos and dumb mistookes!  Much of what's below was written hastily and at odd hours, and was not adequately proofread.   If you find what you believe to be an error in any of these solutions, please let the author know (see below).  It would be appreciated if you included "DE Text Solutions" in the subject line of your email.


4)  Also feel free to send the author any other comments about this webpage or this text.


5)  This material is not in the public domain, and is protected by the copyright laws of the United States.  Viewers of this site have permission to download and use the material being made available here for their personal study.  You, the viewer, may download files, print a few chapters for your personal use, and have links to this website, but please, do not otherwise republish this material without the author's permission.


6)  By the way, "the author" is Dr. Kenneth Howell at the University of Alabama in Huntsville, and can be contacted at .




Solutions to Selected Exercises

Chapter Published /



Part 1 - The Basics   

Chpt 1 - The Starting Point


  typos in 1.3c fixed

Chpt 2 - Integration


 typo in 2.7c fixed 

Part 2 - First-Order Equations 

Chpt 3 - Basics



Chpt 4 - Separable Eqns



Chpt 5 - Linear Eqns



Chpt 6 - Substitution


Chpt 7 - Exact Eqns & Gen Integrating Factors



Chpt 8 - Slope Fields



Chpt 9 - Euler's Num Method


Chpt 10 - Modeling


Part 3 - Higher Order Equations 

Chpt 11 - Extending FIrst-Order Concepts




Chpt 12 - Linear DEs & Reduction of Order


Chpt 13 - Homog DE Soln (General Results) 



Chpt 14 - Homog DE Soln (Verifying & Intro to Lin Operators) 




Chpt 15 - 2nd-Order Const Coeff Eqns


 Error in 8g fixed 

Chpt 16 - Springs: Part I



Chpt 17 - Arb Const Coeff Eqns



Chpt 18 - Euler Eqns



Chpt 19 - Gen Nonhomg Eqns



Chpt 20 - Method of Undet Coeffs



Chpt 21 - Springs: Part II


Chpt 22 - Variation of Parameters



Part 4 - Laplace Transforms         

Chpt 23 - Intro to Laplace Transforms



Chpt 24 - Differentiation & Laplace Transforms



Chpt 25 - Inverse Laplace Transforms



Chpt 26 - Convolution



Chpt 27 - Piecewise-Defined & Periodic Fcts




Chpt 28 - Delta Fcts



Part 5 - Power Series & Modified Power Series Solutions        

Chpt 29 - Review of Series

Chpt 30 - Power Series Solns I (Computational Methods)

Chpt 31 - Power Series Solns II (Generalizations & Theory)

Chpt 32 - Modified Power Series Solns & Frobenius Method

Chpt 33 - Theorems on Frobenius Method w/ Applics

Chpt 34 - Verifying the Theorems on Frobenius Method

There are no exercises in this chapter

Part 6 - Systems of Differential Equations (Brief Intro)        

Chpt 35 - A Starting Point

Chpt 36 - Critical Points, Direction Fields & Trajectories


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Addendum:  According the official policy of the University of Alabama in Huntsville, this website is officially an unofficial UAHuntsville website and is not connected with UAHuntsville.


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Who to Contact If There Is a Reason to Contact the Guy Maintaining This Site:  Prof. Kenneth Howell,