(a) Show that y(x) = Cx4 defines a one-parameter family of differentiable solutions of the...

(a) Show that y(x) = Cx4 defines a one-parameter family of differentiable solutions of the differential equation xy′ = 4y (Fig. 1.1.9). (b) Show that

defines a differentiable solution of xy′ = 4y for all x, but is not of the form y(x) = Cx4. (c) Given any two real numbers a and b, explain why-in contrast to the situation in part (c) of Problem 47-there exist infinitely many differentiable solutions of xy′ = 4y that all satisfy the condition y(a) = b.