The typical 2-point boundary value problem may be written
Two examples are:
In each case, the general solution is 
, and one should solve
for A and B by substitution.
Theorem Consider the function f(x,u,v); if
and 
for all u, v, then the BVP 
has
a unique solution.
Another related class of problems, the so-called eigenvalue problems, may
be suggested by the example: Find all 
such that
.
Speaking in general terms, there are three methods for solving BVPs numerically: shooting, difference methods, and collocation methods. We shall briefly highlight the last of these methods, spending our time on shooting and difference methods.