CHAPTER SUMMARY AND CAUTION
In this chapter, we have considered some simple differential equations
and ways to solve them. Our methods have been graphical, numerical,
and analytical. Equations that we have solved analytically–by
antidifferentiation–have been separable.
It is important to realize that, given a first-order differential equation
of the type , it is the exception, rather than the rule, to be able
to find the general solution by analytical methods. Indeed, a great many
practical applications lead to d.e.’s for which no explicit algebraic
solution exists.