If c ≠ 0, verify that the function defined by y(x) = x/(cx − 1) (with graph illustrated in...

If c ≠ 0, verify that the function defined by y(x) = x/(cx − 1) (with graph illustrated in) satisfies the differential equation x2y′ + y2 = 0 if x ≠ 1 /c. Sketch a variety ot such solution curves for different values of c. Also, note the constant-valued function y(x) = 0 that does not result from any choice of the constant c. Finally, determine (in terms of a and b) how many different solutions the initial value problem x2y′ + y2 = 0, y(a) = b has.