Find Particualr integral of: $\frac{\partial ^3z}{\partial x^3}-4\frac{\partial^3z}{\partial x ^2\partial y}+\frac{\partial ^3 z}{\partial x \partial y^2}-2\frac{\partial^3z}{\partial y^3}=e^{2x+y} $
Soln:
$$P.I=\frac{1}{D^3-4D^2D'+5DD'^2-2D'^3} e^{2x+y}$$
$$\frac{1}{2^3-4.2^2+5.2-2.2^3}e^{2x+y}$$
$$=\frac{-1}{14}e^{2x+y}$$
Please check my solution.
Particular solution is $z=-\dfrac{e^{2x+y}}{8}$