differential equations

Exercise 4 For A E R consider the ODE y" (x) - 2y' (2) + 5y(2) = -Ay(2). (1) (a) Given c E R, use the Laplace transform to find the solution of (1) with y(0) = 0, y'(0) = c. (b) For the differential equation (1) find all eigenfunctions y(x) that satisfy y(0) = 0, y(3) = 0. What are the corresponding eigenvalues