Originally Posted by

**Danny** The second and third are rather straight forward. For the second, the RHS is only a function of y so sek a particular solution in the form $\displaystyle z_p = f(y). $ You'll get an ODE for $\displaystyle f$ (and it's linear!) Similarly for the third. For the first, you'll notice that the RHS is a function of $\displaystyle 2x+y$ so seek $\displaystyle z_p = f(2x+y). $ Since the LHS of the PDEs are independent of both independent variables, this method works.

Hope it helps.