Closed-Form Solution of the Differential Equation (∂2∂x∂y+ax∂∂x+by∂∂y+cxy+∂∂t)P=0 by Normal-Ordering Exponential Operators

A closed‐form solution to Lambropoulos' partial differential equation $$\left(\frac{{\partial }^2}{\mathrm{\partial x\partial y}}\mathrm{+ax}\frac{\partial }{\mathrm{\partial x}}\mathrm{+by}\frac{\partial }{\mathrm{\partial y}}\mathrm{+cxy+}\frac{\partial }{\mathrm{\partial t}}\right)\text{P(x,\hspace{0.17em}y,\hspace{0.17em}t)=0}$$ , subject to the initial condition P(x, y, 0) = Φ(x, y), is presented. The applicability of the normal‐ordering method to a class of partial differential equations is briefly discussed.