Word Count : 604

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The given differential equation is: \[ (x^2 - yx)p + (y^2 - zx)q = z^2 - xy \] We are tasked with finding the equation of the integral surface that passes through the line \( x = 1, y = 0 \). To begin, recall that the notation \( p \) and \( q \) represents partial derivatives, so: - \( p = \frac{\partial z}{\partial x} \) - \( q = \frac{\partial z}{\partial y} \) This implies the equation is a first-order partial differential equation of the form: \[ (x^2 - yx) \frac{\partial z}{\partial x} + (y^2 - zx) \frac{\partial z}{\partial y} = z^2 - xy \] ### Step 1: Using the method of characteristic equations We begin by rewriting _____ _______ __________ ____ ____ ___ __________ ___ ____ ____ _________ __________.
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