Consider the two-dimensional vector field u = = -2x²i+4x(y + xt) j. (a) Show that u could represent the velocity vector field of an incompressible fluid flow. (b) (i) By solving appropriate differential equations, show that the pathlines of this flow for x 0 are described by the equations 1 x = y = 2(t + A)' A 3(t + A) + B(t + A)² - 2' where A and B are arbitrary constants. Hint: Note that t 1 A (t + A)4 (t + A)³ (t + A)4* (ii) For the pathline that passes through the point (½, 3) at time t = 0, eliminate t between the equations given in part (b)(i) to obtain an explicit equation of the form y = y(x) for the pathline.