A planar solenoidal velocity field has the velocity potential

$$\phi(x, y, t)=x e^{-t}+y e^{t}$$

Find and sketch (i) the streamlines at $t=0$; (ii) the pathline that passes through the origin at $t=0$; (iii) the locus at $t=0$ of points that pass through the origin at earlier times (streakline).