4 (a) (10 points) Can et - 1 be the solution of the differential equation of the form y"+ p(t )y' + q(t)y= 0,where p(t) and q(t) are continuous over an open interval containing 0? Justify your answer briefly. (b) (10 points) Let y1 and y2 be solutions of the differential equation x?y" +xy' t (22 - 4)y = 0, x>0 such that yi (1) = y;(1) = 1, y2(1) = 3 and y2(1) = 5. Without computing y1 and y2 explicitly, compute the Wronskian W(y1, y2) as a function of x. (c) (6 points) Let y1 and y2 be functions forming a fundamental pair of solutions to the differential equation y" + p(t)y' + q(t)y = 0, where p(t) and q(t) are continous over an open interval I. Then, there is an equality of Wron- skians W (4y1 + 592, 2y1 + 3y2) = N . W(y1, y2) , where N is a natural number. Compute N. Do 4y1 + 592 and 2y1 + 3y2 form a fundamental pair of solutions