Question 3. Find the general solution of the ODE By"try -rdy=18, where A and B are real numbers. Question 4. Cook up a constant coefficient, homogeneous, 2nd order IVP such that y(r) = e - 4e27 is the solution. Question 5. Can you cook up a real constant coefficient, homogeneous, 2nd order ODE such that y1(r) = ex and y2(r) = sinr are solutions? If not, what about a real constant coefficient, homogeneous, 3rd order ODE? Question 6. Find the only function satisfying the following equation: y" - y = 0, y(1) = 1 and lim y(r) = 0. I-+DO Question 7. Consider the differential operator: L(y) = my" -(x + 1)y + y. a) Verify that er and x + 1 are solution of the homogeneous equation Ly = 0. b) Find a function g(z) satisfying Lg = x2. c) Given a continuous function f(r), find a formula for a function 9, such that Lg = f