The differentiable function p satisfies dxdp=sec2x and passes through the point (43π,2).
(a) Obtain the general solution to the differential equation.
(b) Determine the explicit formula for the particular solution that includes the point (43π,2).
(c) Identify the maximal interval containing 43π on which this particular solution is continuous, and give a brief justification.
(d) Within the interval found in part (c), find all x such that p(x)=5.