Part (a) Solve $(x^2 yz^2) p + 2xy q = 2zx$

To solve this equation, we will attempt to express the relationship among the variables and the constants. The equation is:

$(x^2 yz^2) p + 2xy q = 2zx$

This is a first-order partial differential equation, where $p$ and $q$ are the partial derivatives of a function $u(x, y, z)$, with respect to $x$ and $y$ respectively. To solve this equation, we can apply methods such as the method of characteristics.

We have the following equation: $(x^2 yz^2) \frac{\partial u}{\partial x} + 2xy \frac{\partial u}{\partial y} = 2zx$

This is a first-order linear partial differential equation. A general strategy for solving it would involve:

1. Finding the characteristic equations: The characteristic equations for the PDE are: [ \frac{dx}{x^2 yz^2} = \frac{