Differential Equations Question 130
Question: If $ y=a{x^{n+1}}+b{x^{-n}}, $ then $ x^{2}\frac{d^{2}y}{dx^{2}} $ equals to
[RPET 2001]
Options:
A) $ n(n-1)y $
B) $ n(n+1)y $
C) ny
D) n2y
Show Answer
Answer:
Correct Answer: B
Solution:
$ y=a{x^{n+1}}+b{x^{-n}} $
Differentiate with respect to x , $ \frac{dy}{dx}=a(n+1)x^{n}-bn{x^{-n-1}} $
Again differentiate, $ \frac{d^{2}y}{dx^{2}}=an(n+1){x^{n-1}}+bn(n+1){x^{-n-2}} $
Therefore $ x^{2}\frac{d^{2}y}{dx^{2}}=an(n+1){x^{n+1}}+bn(n+1){x^{-n}} $
Therefore $ x^{2}\frac{d^{2}y}{dx^{2}}=n(n+1)y $ .
BETA
