Consider the Second-Order Differential Equation $\neq$ 0
Which of These Is the Recurrence Relation for the of Frobenius

Multiple Choice

Consider the second-order differential equation .
Suppose the method of Frobenius is used to determine a power series solution of this equation. The indicial equation has r = 0 as a double root. So, one of the solutions can be represented as the power series .
Assume a₀ $\neq$ 0.
Which of these is the recurrence relation for the coefficients?

A) $a_{1}=0, a_{n}=-\frac{64 \cdot a_{n-2}}{2^{n}}, n \geq 2$
B) $a_{1}=1, a_{n}=\frac{64 \cdot a_{n-2}}{2^{n}}, n \geq 2$
C) $a_{1}=1, a_{n}=\frac{64 \cdot a_{n-2}}{n^{2}}, n \geq 2$
D) $a_{1}=0, a_{n}=-\frac{64 \cdot a_{n-2}}{n^{2}}, n \geq 2$
E) $a_{1}=0, a_{n}=-\frac{64 \cdot a_{n-2}}{n}, n \geq 2$