A differentiable function y=f(x) satisfies the differential equation dxdy=ysinx for all real x. The graph of f passes through the point (0,3).
(a) Determine the general solution of the differential equation. Express your answer in explicit form.
(b) Using the initial condition, find the particular solution that passes through (0,3).
(c) State the maximal interval containing x=0 on which your particular solution is defined and differentiable. Justify your answer briefly.