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 = x0 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 (D2 5D 6)y = 0
A.E is m2 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;
c1 = 15 and c2 = -15