Exact analytic solutions of unsolvable classes of first- and second-order nonlinear ODEs (Part II: Emden–Fowler and relative equations) Original Research Article

Both Emden–Fowler and generalized Emden–Fowler nonlinear ordinary differential equations (ODEs) are reduced to Abel’s equation of the second kind by means of admissible functional transformations. Since in Part I a mathematical technique is developed leading to the construction of exact analytic solutions of the above Abel equation, it follows that the Emden–Fowler equations admit exact analytic solutions too. In this sense several basic particular nonlinear ODEs in mathematical physics are examined.