Solve x2(y-z)p + y2(z-x)q = z2(x-y).

Here are the solutions for the given partial differential equations.

a) Solve $x^2(y-z)p + y^2(z-x)q = z^2(x-y)$.

This is a first-order linear partial differential equation of the form $Pp + Qq = R$, which can be solved using Lagrange's method of characteristics.
The auxiliary equations are given by:

$$\frac{dx}{P} = \frac{dy}{Q} = \frac{dz}{R}$$

Substituting the given values:

$$\frac{dx}{x^2(y-z)} = \frac{dy}{y^2(z-x)} = \frac{dz}{z^2(x-y)}$$