If you are seeking a text which deals specifically with differential
equations, you may wish to consider the following 160 page
e-book compilation done up by my good friend Karl Hahn in
2009 and made free online for the benefit of others:
GUIDE TO SOLVING DIFFERENTIAL EQUATIONS
In his email to me, he provided a succinct synopsis of his work:
"It consists of text extracted from the 1902 J.W. Mellor
text book together with my supplement containing
step-by-step worked solutions to most of the problems
as well as my presentations of alternative methods not
covered in the text-Karl "
In particular, this written guide dishes out detailed advice with
regards to solving first order/ higher order/partial/simultaneous
differential equations; it also examines the applications of DEs in
the context of mechanics, thermodynamics and chemical reactions.
I am highly selective when it comes to recommendation of books,
and honestly this is really good stuff. Peace.