The differential equation dxdy=2x+1 has general solution y=x2+x+C. Can a single particular solution of this equation pass through both points (0,3) and (1,8)?
(a) Yes; choosing C=3 satisfies both points.
(b) No; the two points require different constants, so no such curve exists.
(c) No; the slope at x=0 implied by the points contradicts the differential equation.
(d) Yes; because a first-order differential equation has infinitely many solutions, so one must pass through any two given points.