[Ex] A steady, two-dimensional, incompressible flow field in the \(xy\)-plane has a stream function given by \(\psi = ax^3 + by + cx\), where \(a\), \(b\), and \(c\) are constants: \(a = 0.50\) \((m\cdot s)^{-1}\), \(b = -2.0\text{ m/s}\), and \(c = -1.5\text{ m/s}\).

(1) Obtain expressions for velocity components \(u\) and \(v\).

(2) Verify that the flow field satisfies the incompressible continuity equation.

(3) Plot several streamlines of the flow in the upper-right quadrant.