In a recent paper by R. A. Handelsman and J. S. Lew [1], it is shown that for a certain family of potentials, the eigenvalues of the one-dimensional time-independent Schrödinger equation are proportional to $u(x,y)^{ - 2} $ with u determined by $u^{1/\beta } = f(xu,yu^{2/\beta })$, where $f(x,y) = \sum_{r = 0}^\infty \sum_{s = 0}^\infty f_{rs} x^s y^r $. Both $\beta $ and the $f_{rs} $ are known constants, with $f_{00} = 1$. In [2], Lew proposed that a system for symbolic algebra be used to compute the Taylor series expansion for $u(x,y)$, although in [1] what is desired is the expansion of $c(x,y) = u(x,y)^{ - 2} $. To illustrate how such a system can be used to solve this and similar problems, three solution methods are described and corresponding programs given. During the attempt to put the output resulting from these programs into a form similar to that given by Lew [1], the general solution was found. We give this solution here but defer the proof to another paper [3].