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To solve the given first-order partial differential equation (PDE) using Charpit's method, we have the equation: \[ p(1 + q^2) + (b - z)q = 0, \] where \( p = \frac{\partial z}{\partial x} \) and \( q = \frac{\partial z}{\partial y} \), and \( b \) is a constant. ### Step 1: Characteristic Equations Charpit's method involves finding the characteristic equations for the PDE. The general form of the characteristic equations is: \[ \frac{dx}{ds} = ________ _______ _____ ________ ____.
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