Assignment:
Consider the equation: y’’ + k*y = 0 with BC: y(0) = 0 , y(π) = a ≠0
Answer the following:
Q1. What are the restrictions on k such that there is a nontrivial solution?
Q2. Find a solution using eigenfunction expansion on [0,π]
Q3. Find a solution to the differential equation using any method
Q4. Compare answers 2 and 3 show they are equivalent
Provide complete and step by step solution for the question and show calculations and use formulas.