First Integrals Without Integrating Factors or Symmetries

A new method to find first integrals of ordinary differential equations (ODEs) is presented. The approach is based on the complete integrability of the Pfaffian system associated with the ODE, and it does not require the use of symmetries or integrating factors. Examples of second-, third-, and fourth-order ODEs are provided to illustrate the method, including cases where classical approaches fail. This work extends the range of tools available for the analysis and solution of ODEs.