Consider the differential equation
dxdy=xy2,
where y is a differentiable function of x. The solution curve is known to pass through the point (2,3).
(a) Solve the differential equation to obtain the general solution y(x).
(b) Use the point (2,3) to determine the particular solution that satisfies the given condition.
(c) State the largest interval, containing x=2, on which your particular solution is valid. Justify your answer briefly.