Chapter 2, Problem 13P

For the velocity field $\stackrel{\to }{V}=Ax\hat{i}-Ay\hat{j},$, where A = 2s ⁻¹. which can be interpreted to represent flow in a corner, show that the parametric equations for particle motion are given by x_p = c₁ e^At and y_p = c₂ e^−At. Obtain the equation for the pathline of the particle located at the point (x, y) = (2, 2) at the instant t = 0. Compare this pathline with the streamline through the same point.