Parametrically defined nonlinear differential equations and their solutions: Applications in fluid dynamics

The study deals with parametrically defined ordinary differential equations, practically unaddressed in the literature. It finds the general solutions for three classes of first- and second-order nonlinear ODEs of this kind. The solutions are further used to construct new exact solutions to the equations of an unsteady axisymmetric boundary layer with pressure gradient on a body of revolution of arbitrary shape. Also the paper suggests a short list of essential problems for nonlinear ODEs and PDEs defined parametrically that need to be addressed in the future.