Show that this nonlinear equation is valid for transonic flow with small perturbations: [left(1-M_{infty}^{2} ight) frac{partial^{2} phi}{partial

Show that this nonlinear equation is valid for transonic flow with small perturbations:

\[\left(1-M_{\infty}^{2}\right) \frac{\partial^{2} \phi}{\partial x^{2}}+\frac{\partial^{2} \phi}{\partial y^{2}}+\frac{\partial^{2} \phi}{\partial z^{2}}=M_{\infty}^{2}\left[\frac{\gamma+1}{V_{\infty}} \frac{\partial \phi}{\partial x}\right] \frac{\partial^{2} \phi}{\partial x^{2}}\]