Consider the second-order differential equation: .
Which of these is the recurrence relation for the coefficients?
A) $ a_{n}=\frac{-2(n+r-1) a_{n-1}}{(2(n+r)+5)(n+r+1)}, n \geq 1 $
B) $ a_{n}=\frac{2(n+r-1) a_{n-1}}{(2(n+r)-5)(n+r+1)}, n \geq 1 $
C) $ a_{n}=\frac{-2(n+r-1) a_{n-1}}{(2(n+r)-1)(n+r+5)}, n \geq 1 $
D) $ a_{n}=\frac{2(n+r-1) a_{n-1}}{(2(n+r)+1)(n+r-5)}, n \geq 1 $

Question

Consider the second-order differential equation:  .
Which of these is the recurrence relation for the coefficients?
A) $ a_{n}=\frac{-2(n+r-1) a_{n-1}}{(2(n+r)+5)(n+r+1)}, n \geq 1 $ 
B) $ a_{n}=\frac{2(n+r-1) a_{n-1}}{(2(n+r)-5)(n+r+1)}, n \geq 1 $ 
C) $ a_{n}=\frac{-2(n+r-1) a_{n-1}}{(2(n+r)-1)(n+r+5)}, n \geq 1 $ 
D) $ a_{n}=\frac{2(n+r-1) a_{n-1}}{(2(n+r)+1)(n+r-5)}, n \geq 1 $

Quizplus · Accepted Answer

The Answer of Consider the second-order differential equation:  .
Which of these is the recurrence relation for the coefficients?
A) $ a_{n}=\frac{-2(n+r-1) a_{n-1}}{(2(n+r)+5)(n+r+1)}, n \geq 1 $ 
B) $ a_{n}=\frac{2(n+r-1) a_{n-1}}{(2(n+r)-5)(n+r+1)}, n \geq 1 $ 
C) $ a_{n}=\frac{-2(n+r-1) a_{n-1}}{(2(n+r)-1)(n+r+5)}, n \geq 1 $ 
D) $ a_{n}=\frac{2(n+r-1) a_{n-1}}{(2(n+r)+1)(n+r-5)}, n \geq 1 $

Consider the Second-Order Differential Equation an=−2(n+r−1)an−1(2(n+r)+5)(n+r+1),n≥1 a_{n}=\frac{-2(n+r-1) a_{n-1}}{(2(n+r)+5)(n+r+1)}, n \geq 1 an​=(2(n+r)+5)(n+r+1)−2(n+r−1)an−1​​,n≥1

Consider the Second-Order Differential Equation $a_{n}=\frac{-2(n+r-1) a_{n-1}}{(2(n+r)+5)(n+r+1)}, n \geq 1$