questions below:

d Consider the differential equation 4yy - 9x = 0, which has a oneparameter family of implicit solutions 9x2 - 4y2 = C for every constant 0' Complete parts (a) through (1:) below. dx (a) Does the Existence and Uniqueness of Solution Theorem imply the existence of a unique solution to the differential equation that satises y(xo) = 0? Select the correct choioe below and, if necessary, ll in the answer box within your choice 0 A. The theorem does not imply the existence of a unique solution for any values of x0. 0 B. The theorem implies the existence of a unique solution for all values of XO. O C. The theorem implies the existence of a unique solution only for values of XO in the interval (Type your answer in interval notation) (b) Show that when x0 # 0, the differential equation can't possibly have a solution in a neighborhood of x =x0 that satises y (x0) = 0' Substituting the initial condition into the differential equation gives 4 - 9 = 0. This equation can be simplied to i which V the given condition that |