Differential Equations For Dummies

I bought this book last night. Now having skimmed through it, I horribly regret it. I don't have all that extensive back ground in diff. eq. but the errors were so terribly obvious to me. The main portion that really upset me was when the author was showing how a laplace transform diverges. His conclution is correct, but his solution to arrive at that conclusion is incorrect. The author gets the answer te^(-s). The answer should be e^[t(1-s)]/(1-s). Yes these have the same limit at infinity, but only when s