Difference between Initial value conditions problem and boundary value conditions problem
In initial value problem we are given the derivative of a function say f(x) at one point i.e. for example f\'(x) at x=2 will be specified(at x=2 f\'(x)=1) or something like that.But for a boundary value problem slope at two points will be specified,for example if we consider the previous example f\'(2) and f\'(4) will be specified.
In general it is easier to solve boundary condition problem for different equations whose degree is greater than or equal to 2.