Closed-form meromorphic solutions of some third order boundary layer ordinary differential equations

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 Cheng-Minkowycz equation. Using Wiman-Valiron theory complex analytic methods recently developed, for generic cases, it is shown that all their meromorphic solutions must be rational, or rational in one exponential, then we find of them explicitly. For few non-generic some solutions, are singlevalued, also obtained. Our results explain why so difficult to obtain new closed-form