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Let's go step by step to solve these problems. ### (a) Verify Integrability and Find the Integral The given Pfaffian differential equation is: \[ yz\,dx + (x^2y - zx)\,dy + (x^2z - xy)\,dz = 0 \] A first-order Pfaffian equation of the form: \[ Pdx + Qdy + Rdz = 0 \] is integrable if the Frobenius condition is satisfied, which states that: \[ \frac{\partial Q}{\partial z} - \frac{\partial R}{\partial y} = 0, \quad \frac{\partial R}{\partial x} __________ ________ ______ _________ __________ _____ ____.
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