An exact solution to the transonic equation

The small disturbance equation of transonic flow is solved by a separation of variables technique. The resulting ordinary, nonlinear differential equations are studied in the phase plane where the general solution represents the behavior of the perturbation velocities. In the phase plane, the character of transonic flow is evident. An asymptotic explicit solution is given which encompasses the sonic flow solution. Numerical integration results for the implicit equations are presented and two flows are examined which are intrinsic to the form of the solution.