Problems in Differential Equations

A supplement for elementary and intermediate courses in differential equations, this text features more than 900 problems and answers. Suitable for undergraduate students of mathematics, engineering, and physics, this volume also represents a helpful tool for professionals wishing to brush up on their problem-solving skills.
The book is divided into twenty sections, each preceded by a clear and logical explanation of the basic ideas needed for solving the problems within the section. Many fully explained illustrative problems appear throughout the text. Subjects include applied routine and nonroutine problems in vibrations, electrical engineering, mechanics, and physics. Stars indicate advanced problems. Short mathematical and numerical tables are provided at the end of the book.

Mathematician and Professor of Mathematics Joel Lee Brenner (1912–97) specialized in matrix theory, linear algebra, and number theory.

Preface

Introduction

1. Isoclines, Construction of the Differential Equation for a Family of Curves Isogonal Trajectories

2. Equations in which the Variables are Separable

3. Geometrical and Physical Problems

4. Homogeneous Equations

5. Linear First Order Equations

6. Exact Equations

7. Questions on Existence and Uniqueness of Solutions

8. Equations in which the Derivative Appears Implicitly

9. Miscellaneous First Order Equations

10. Equations which can be Reduced to Equations of Lower Order

11. Linear Equations with Constant Coefficients

12. Linear Equations with Variable Coefficients

13. Series Development of Solutions of Equations

14. Linear Systems with Constant Coefficients

15. Lyapunov Stability

16. Singular Points

17. Problems in the Theory of Oscillations

18. Dependence of Solutions on Initial Conditions and on Parameters. Approximate Solution of Differential Equations

19. Non-Linear Systems

20. First Order Partial Differential Equations

Answers

Miscellaneous Formulas

Derivatives

Some Integrals

Tables: Square Roots, Cube Roots

Logarithms

Exponentials

Trigonometric Functions