  A quantization procedure, which has recently been introduced for the analysis
of Painlev\'e equations, is applied to a general time-independent potential of
a Newton equation. This analysis shows that the quantization procedure
preserves the exact solvability property for the class of shape-invariant
potentials. When a general potential is considered the quantization procedure
involves the solution of a Gambier XXVII transcendental equation. Explicit
examples involving classical and exceptional orthogonal Laguerre and Jacobi
polynomials are discussed.
