Answer to Question #204417 in Differential Equations for smi

Question

How is a BVP different from IVP?

Answer 1

Initial Value Problem (IVP):

In initial value problems, we are given the value of function $y(x)$ and its derivative $y'(x)$ at the same point (initial point), say at $x=0$ , that is:

$$y(0)=x_1 \text{ and } y'(0)=x_2$$

while

Boundary Value Problem (BVP):

In boundary value problem, we are given the value of function $y(x)$ at two different points, that is:

$$y(a)=x_1 \text{ and } y'(b)=x_2$$