  This paper aims to demonstrate the applicability of the L_2-integral
transform to Partial Differential Equations (PDEs). Of special interest is
section (6), which contains an application of the L_2-transform to a PDE of
exponential squared order, but not of exponential order. Sections (1) and (2)
aim to introduce the history and some elementary properties of the
L_2-transform, (3) and (4) include some of the transform's simple applications,
and section (5) introduces the L_2 convolution.
