# Solution Of Initial And Boundary Value Function

**Solution of Initial and Boundary Value Function:**

The differential equation in which the conditions are specified at a single value of the independent variable say x = x_{0} is called an Initial Value Problem (IVP). If y = y(x), the initial conditions usually will be of the form.

The differential equation in which the conditions are specified for a given set of n values of the independent variables is called Boundary Value Problems (BVP).

We can also have problems involving a system of (simultaneous de.s) with these types of conditions.

**Problems on Initial and Boundary Value Function:
**

**1**. Solve the initial value problems given that

**Solutions:** We have (D^{2} 5D 6)y = 0

A.E is m^{2} 5m 6 = 0

(m 2) (m 3) = 0

⇒ m = -2,-3

General equation is

This is the General solution of the given equations;

Also we have the above equations;

Apply the condition:

We obtain the following equatins;

.........(3)

Solving equation (2) and (3) we get;

c_{1 }= 15 and c_{2 }= -15