Assuming that dp/dx = 0, show that Eq. 8.6.47 follows from Eq. 8.6.45.
u \frac{\partial u}{\partial x}+v \frac{\partial u}{\partial y}=-\frac{1}{\rho} \frac{d p}{d x}+\nu \frac{\partial^{2} u}{\partial y^{2}} (8.6.45)
\frac{\partial \psi}{\partial y} \frac{\partial^{2} \psi}{\partial x \partial y}-\frac{\partial \psi}{\partial x} \frac{\partial^{2} \psi}{\partial y^{2}}=\nu \frac{\partial^{3} \psi}{\partial y^{3}} (8.6.47)