  The Ramanujan Machine project predicts new continued fraction representations
of numbers expressed by important mathematical constants. Generally, the value
of a continued fraction is found by reducing it to a second order linear
difference equation. In this paper, we prove 38 conjectures by solving the
equation in two ways, use of a differential equation or application of
Petkov\v{s}ek's algorithm. Especially, in the former way, we can get strong
generalization of 31 conjectures.
