Consider the differential equation dxdy=sec2x−2x with the condition that the solution passes through the point (4π,3).
Answer all parts, showing each step of your reasoning.
(a) Determine the general solution y=F(x) of the differential equation.
(b) Use the given point to find the particular solution that satisfies the condition.
(c) State the largest open interval containing x=4π on which your particular solution is valid, and justify your choice based on the behavior of the integrand in part (a).