For Problems 24–26, solve the given initial-value problem. (a) Show that the genera...

For Problems 24–26, solve the given initial-value problem.

(a) Show that the general solution to the differential equation

(b) For the particular case when a = 1/2, determine the solution satisfying the initial condition y(1) = 1, and find the maximum x-interval on which this solution is valid. [Hint: When does the solution curve have a vertical tangent?]

(c) On the same set of axes, sketch the spiral corresponding to your solution in (b), and the line y = x/2. Thus verify the x-interval obtained in (b) with the graph.