1. The problem involves the expression $$\oint 2xy \frac{dy}{dx} + 2y^2 - 3x - d$$ which appears to be a line integral or a differential expression involving $x$, $y$, and their derivatives. 2. To analyze or solve this, we need to clarify the context: is this an integral over a closed curve, a differential equation, or something else? Assuming it's a differential equation or expression, let's consider the terms. 3. The term $$2xy \frac{dy}{dx}$$ involves the derivative of $y$ with respect to $x$, multiplied by $2xy$. 4. The expression $$2y^2 - 3x - d$$ is algebraic in $x$ and $y$, with $d$ presumably a constant. 5. If the goal is to solve for $\frac{dy}{dx}$, rearrange the expression: $$2xy \frac{dy}{dx} = -2y^2 + 3x + d$$ 6. Then, $$\frac{dy}{dx} = \frac{-2y^2 + 3x + d}{2xy}$$ 7. This is a first-order differential equation for $y$ in terms of $x$. 8. To solve it, one might attempt separation of variables or an integrating factor, depending on the function forms. 9. Without further context or boundary conditions, this is the simplified form of the derivative. Final answer: $$\frac{dy}{dx} = \frac{-2y^2 + 3x + d}{2xy}$$