I will solve the questions one by one. Let's start with Q1.

Q1: Solve $(y + zx)p - (x + yz)q = x^2 - y^2$

This is a first-order partial differential equation in standard form: $p = \frac{\partial z}{\partial x}, \quad q = \frac{\partial z}{\partial y}$ The general form of the equation can be written as: $(y + zx)p - (x + yz)q = x^2 - y^2$ This can be solved using the method of characteristics. We rewrite the equation in characteristic form: $\frac{dx}{y + zx} = \frac{dy}{-(x + yz)} = \frac{dz}{x^2 - y^2}$ To solve this, let's break it down step by step.

1. Solving $\frac{dx}{y + zx} = \frac{dy}{-(x + yz)}$: The cross multiplication of these terms gives: $(y + zx)dy + (x + yz)dx = 0$ Expanding the terms: $ydy + zxdx + xdx + yzdx = 0$ Combine like terms: $ydy + xdx + (zx + yz)dx = 0$ Simplify and separate variables to find the characteristic curves.

2. Solve $\frac{dz}{x^2 - y^2}$.

By solving these, we will find the general solution for $z$.

I will continue solving step by step. Would you like the detailed process for the first equation or should I proceed to another question? Let me know if you have any specific queries.