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

摘要

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. (c) 2004 Elsevier Ltd. All rights reserved.