The Case of Missing Solutions of an Ordinary Differential Equation

This short paper offers a new technique to extract independent solutions from a certain type of ordinary differential equation which would frequently refuse to declare all the solutions under conventional infinite series treatment. This new mathematical tool, most suited for differential equations with elusive solutions, is not found in the mathematics courses taken by a first-year graduate student in Engineering. It should, therefore, be of special interest to him, when he is in the dilemma of deciding whether he has an oversupply of boundary conditions or a shortage of arbitrary constants. Assuming that the differential equation is not in error, he is most likely negligent in not having claimed all the independent solutions from the differential equation. The new technique described in this paper may help remedy this situation.