Problem 46E

Use the result in Problem 45 to solve

(reference problem 45)

Suppose the solution of the boundary-value problem and are solutions of the associated homogeneous differential equation chosen in the construction of so that Prove that the solution of the boundary-value problem with nonhomogeneous DE and boundary conditions, is given by

[Hint: In your proof, you will have to show that Re read the assumptions following (24).]

Solution :

Step 1 :

In this problem we have to find the given differential equation by using boundary-value problem.

Given differential equation is and ,

The homogeneous differential equation is