CSIR NET Maths previous year question papers

For any non-zero solution y = y(x) of the differential equation $(2x + 3)^{2}(d^{2}y/$dx$^{2}) + 6(2x + 3)($dy/dx) + 8y = 0, x > 0, denote S := {$x \in (0, \infty) : y(x) = 0$}. Then

Let $\mathbb{C}[x, y]$ be the polynomial ring in two variables over $\mathbb{C}$. For which of the following ideals I, the quotient ring $\mathbb{C}[x, y]/I$ is NOT an integral domain?