I used an earlier version of Boyce & DiPrima and hated it like most everyone else here. (Why is it that all the crappy textbooks live on, edition-after-edition, inflicted on a new batch of students year-after-year?) To get through my DE course I used the book by Dennis G. Zill. It was pretty good. Zill's book is still around. Comes in several different flavors.

For those looking for a better book than Boyce/Diprima I've listed all recent, introductory DE books I could find on amazon:

"An Introduction to Ordinary Differential Equations" by James C. Robinson (ISBN 0521533910). This provides a very gentle introduction. does not cover Laplace transforms.

Shepley L. Ross has 2 books: an intro book (Introduction to Ordinary Differential Equations, 4th Edition ISBN: 978-0-471-09881-2) and a regular text (Differential Equations, 3rd Edition, ISBN: 978-0-471-03294-6) which have garnered good reviews.

Can also try "Elementary Differential Equations" by Kohler and Johnson.

Physical Science/Engineering/applications oriented:

2 books by John Polking (one on DEs and one on ODEs/BVPs)
Elementary Differential Equations by William Trench
Fundamentals of Differential Equations by Nagle, Saff & Snider
An Introduction to Differential Equations and Their Applications by Stanley J. Farlow (ISBN 048644595X). He's also got a PDE book.

For the engineers: you might want to skip a separate DE book altogether and get a combined book. Something like Linear Algebra and Differential Equations by Peterson and Sochacki

OR just get all of Ken Stroud's engineering math books:

"Engineering Mathematics" by K.A. Stroud, Dexter Booth
"Advanced Engineering Mathematics" by K.A. Stroud, Dexter Booth
"Differential Equations" by K.A. Stroud, Dexter Booth
"Vector Analysis" by K.A. Stroud, Dexter Booth
"Linear Algebra" by K.A. Stroud, Dexter Booth
"Complex Variables" by K.A. Stroud, Dexter Booth

other options: "Differential Equations Demystified" by Steven G. Krantz / "2500 Solved Problems in Differential Equations" (Schaum's Solved Problems Series) by Richard Bronson / The Differential Equations Problem Solver ISBN 0878915133

Two books that involve computer/numerical methods would be:

1. A Modern Introduction to Differential Equations by Henry Ricardo
2. Differential Equations: An Introduction to Modern Methods and Applications by James R. Brannan, William E. Boyce. Although, I'd be leery of any DE book with Boyce as an author.

Of course, Dover Publications has inexpensively reprinted boatloads of classic math books including these DE titles:

"Ordinary Differential Equations" by Morris Tenenbaum, Harry Pollard. (rated highly)

Plus in addition to the Farlow book they have:

An Introduction to Ordinary Differential Equations by Earl A. Coddington
Introduction to Linear Algebra and Differential Equations by John W. Dettman
Differential Equations: A Concise Course by H. S. Bear
I used an earlier version of Boyce & DiPrima and hated it like most everyone else here. (Why is it that all the crappy textbooks live on, edition-after-edition, inflicted on a new batch of students year-after-year? ) To get through my DE course I used the book by Dennis G. Zill. It was pretty good. Zill's book is still around. Comes in several different flavors. For those looking for a better book than Boyce/Diprima I've listed all recent, introductory DE books I could find on amazon:

"An Introduction to Ordinary Differential Equations" by James C. Robinson (ISBN 0521533910). This provides a very gentle introduction. does not cover Laplace transforms. Shepley L. Ross has 2 books: an intro book (Introduction to Ordinary Differential Equations, 4th Edition ISBN: 978-0-471-09881-2) and a regular text (Differential Equations, 3rd Edition, ISBN: 978-0-471-03294-6) which have garnered good reviews. Can also try "Elementary Differential Equations" by Kohler and Johnson. Physical Science/Engineering/applications oriented:

2 books by John Polking (one on DEs and one on ODEs/BVPs)
Elementary Differential Equations by William Trench
Fundamentals of Differential Equations by Nagle, Saff & Snider
An Introduction to Differential Equations and Their Applications by Stanley J. Farlow (ISBN 048644595X). He's also got a PDE book. For the engineers: you might want to skip a separate DE book altogether and get a combined book. Something like Linear Algebra and Differential Equations by Peterson and Sochacki

OR just get all of Ken Stroud's engineering math books:

"Engineering Mathematics" by K. A. Stroud, Dexter Booth
"Advanced Engineering Mathematics" by K. A. Stroud, Dexter Booth
"Differential Equations" by K. A. Stroud, Dexter Booth
"Vector Analysis" by K. A. Stroud, Dexter Booth
"Linear Algebra" by K. A. Stroud, Dexter Booth
"Complex Variables" by K. A. Stroud, Dexter Booth

other options: "Differential Equations Demystified" by Steven G. Krantz / "2500 Solved Problems in Differential Equations" (Schaum's Solved Problems Series) by Richard Bronson / The Differential Equations Problem Solver ISBN 0878915133

Two books that involve computer/numerical methods would be:

1. A Modern Introduction to Differential Equations by Henry Ricardo
2. Differential Equations: An Introduction to Modern Methods and Applications by James R. Brannan, William E. Boyce. Although, I'd be leery of any DE book with Boyce as an author. Of course, Dover Publications has inexpensively reprinted boatloads of classic math books including these DE titles:

"Ordinary Differential Equations" by Morris Tenenbaum, Harry Pollard. (rated highly)

Plus in addition to the Farlow book they have:

An Introduction to Ordinary Differential Equations by Earl A. Coddington
Introduction to Linear Algebra and Differential Equations by John W. Dettman
Differential Equations: A Concise Course by H. S. Bear