Differential Equations Question 126
Question: The elimination of the arbitrary constants A, B and C from $ y=A+Bx+C{e^{-x}} $ leads to the differential equation
[AMU 1999]
Options:
A) $ {{{y}’}’}’-{y}’=0 $
B) $ {{{y}’}’}’-{{y}’}’+{y}’=0 $
C) $ {{{y}’}’}’+{{y}’}’=0 $
D) $ {{y}’}’+{{y}’}’-{y}’=0 $
Show Answer
Answer:
Correct Answer: C
Solution:
Given $ y=A+Bx+C{e^{-x}} $ ……..(i)
Therefore $ \frac{dy}{dx}=B-C{e^{-x}} $ ……..(ii)
Therefore $ \frac{d^{2}y}{dx^{2}}=C{e^{-x}} $ ……..(iii) and $ \frac{d^{3}y}{dx^{3}}=-C{e^{-x}} $ …….(iv)
Adding (iii) and (iv) we get,
$ \frac{d^{3}y}{dx^{3}}+\frac{d^{2}y}{dx^{2}}=0 $ i.e., $ {y}’’’+{y}’’=0 $ .
BETA
