particular integral in partial differential equation Solve the partial differential equation
$$\left[D^2+{D^\prime}^2\right]z=\cos mx\cdot\cos ny.$$
I have a problem in finding particular integral where $\displaystyle\frac\partial{\partial x}=D$ and $\displaystyle\frac\partial{\partial y}=D^\prime$.

Hint:-$\frac{1}{2}(2cosmx.cosny)=\frac{1}{2}[cos(mx-ny)+cos(mx+ny)]$
and $\frac{1}{D^2+D'^2} cos(mx+ny)=\frac{cos(mx+ny)}{-m^2-n^2}$
