Word Count : 410

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Let's solve these three differential equations one by one. ### i) \(\frac{dx}{y^2(x-y)} = \frac{dy}{x^2(x-y)} = \frac{dz}{z(x^2+y^2)}\) This is a system of equations, and we can treat it in the form of a parametric equation. Let's use a parameter \( t \) and express each of the differential equations with respect to \( t \): \[ \frac{dx}{y^2(x-y)} = \frac{dy}{x^2(x-y)} = \frac{dz}{z(x^2+y^2)} = t \] So, we have: 1. \( \frac{dx}{y^2(x-y)} = t \) ⟹ \( dx = t \cdot y^2(x-y) dt \) 2. \( \frac{dy}{x^2(x-y)} = t \) ⟹ \( dy = t \cdot x^2(x-y) dt \) 3. \( \frac{dz}{z(x^2+y^2)} = t \) _______ ___ ________ ______ ___ _______ _________ ______ ___.
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