(a) Sketch the vector field F(x, y) = i + x j and then sketch some flow lines. What shape do these flow lines appear to have?
(b) If parametric equations of the flow lines are x = x(t), y = y(t), what differential equations do these functions satisfy? Deduce that dyydx = x.
(c) If a particle starts at the origin in the velocity field given by F, find an equation of the path it follows.