The given differential equation is: \[ \left( 4X^{3} y^{3} + \frac{1}{X} \right) dX + \left( 3X^{4} y^{2} - \frac{1}{y} \right) dy = 0. \] This is a first-order, partial differential ______ ______ _________ ___ ___ __________ _________ _________ ____ _____.
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