1. The problem statement, all variables and given/known data a) Solve for the BVP. Where A is a real number. b) For what values of A does there exist a unique solutions? What is the solution? c) For what values of A do there exist infintely many solutions? d) For what values of A do there exist no solutions? 2. Relevant equations y'' + y = A + sin(2x) y(0) = y'([tex]\pi[/tex]/2) = 2 3. The attempt at a solution y = yh + yp 0 = 1+ [tex]\lambda[/tex]2 yh =c1*cos(x) + c2*cos(x) yp = A + B*sin(2x) y = A + B*sin(2x) y'' = -4B*sin(2x) A + sin(2x) = A -3B*sin(2x) A = A, B = -1/3 yp = A - 1/3*sin(2x) y = A - 1/3*sin(2x) + c1*cos(x) + c2*sin(x) y' = - 2/3*sin(2x) - c1*sin(x) + c2*cos(x) 2 = A + c1 2 = 2/3 + c2 c2 = 8/3 y = A - 1/3*sin(2x) + c1*cos(x) + 8/3*sin(x) I'm confused about answering the questions. A would be equal to all real numbers, since one could solve for c1. How can I give the solution? There is a unique solution for each value of A, which I would have to write infinte solutions. And there is no value of A when there is an inifiite amount of solutions or no values. IF A is defined, what would the answer be?