## ABSTRACT

Solutions of linear differential equations of order n together with n conditions specified on the dependent variable and its first (n-I) derivatives at an initial point were discussed in Section ( I.8) and were referred to as Initial Value Problems. It was shown that the solutions to such problems are unique and valid over the range of all values of the independent variable. If the differential equation as well as the Initial Condition are homogeneous, then it can be shown that the solutions to such problems vanish identically. In this chapter, solutions to linear differential equations of order n with n conditions specified on two end points of a bounded region valid in the closed region between the two end points, will be explored. These points are called Boundary Points,

st and the conditions on the dependent variable and its derivatives up to the (n-I) are called Boundary Conditions (BC). Such problems are referred to as Boundary Value Problems (BVP).