Exact solutions of a third-order ODE from thin film flow using λ-symmetry method

摘要

We obtain exact implicit solutions of the third order ordinary differential equation y~m =y~(-n) for the first time. These exact solutions are obtained using λ-symmetry reduction method, when n = (5/2) and n = (5/4). The obtained solutions are valid for the general initial conditions y(α) = y, y'(α) = δ, y"(α) = β. It is shown that the contact angle Ø=90° when n = (5/2), and it varies with the initial conditions when n=(5/4).