  We introduce a general third order non-linear autonomous ODE which covers
many ODEs coming from boundary layer problems, like the Falkner-Skan equation
and the Cheng-Minkowycz equation. Using Wiman-Valiron theory and complex
analytic methods recently developed, for the generic cases, it is shown that
all their meromorphic solutions must be rational, or rational in one
exponential, and then we find all of them explicitly. For a few non-generic
cases, some solutions, which are meromorphic or singlevalued, are also
obtained. Our results also explain why it is so difficult to obtain new
closed-form solutions of the Falkner-Skan equation.
