Consider the Second-Order Differential Equation $x^{2} p(x)$ And $x q(x)$

Multiple Choice

Consider the second-order differential equation .
Write the differential equation in the form . a regular singular point for this equation?

A) $x^{2} p(x)$ and $x q(x)$ both have convergent Taylor expansions about 0 .
B) $\lim _{x \rightarrow 0} x^{2} p(x) =0$ and $\lim _{x \rightarrow 0} x q(x) =\infty$
C) $\lim _{x \rightarrow 0} x p(x)$ is finite and $\lim _{x \rightarrow 0} x^{2} \gamma(x) =\infty$
D) $\lim _{x \rightarrow 0} x p(x)$ is finite and $x^{2} \gamma(x)$ has a convergent Taylor expansion about 0 .