Differentiation Question 361
Question: If $ y=ae^{mx}+b{e^{-mx}} $ , then $ \frac{d^{2}y}{dx^{2}}-m^{2}y= $
[MP PET 1987]
Options:
A) $ m^{2}(ae^{mx}-b{e^{-mx}}) $
B) 1
C) 0
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ y=ae^{mx}+b{e^{-mx}}; $
$ \therefore \frac{dy}{dx}=ame^{mx}-mb{e^{-mx}} $
Again $ \frac{d^{2}y}{dx^{2}}=am^{2}e^{mx}+m^{2}b{e^{-mx}} $
Therefore $ \frac{d^{2}y}{dx^{2}}=m^{2}(ae^{mx}+b{e^{-mx}})\Rightarrow \frac{d^{2}y}{dx^{2}}=m^{2}y $
or $ \frac{d^{2}y}{dx^{2}}-m^{2}y=0 $ .
BETA
