Differential Equations Question 100
Question: The differential equation whose solution is $ y=A\sin x+B\cos x, $ is
[CEE 1993; Kerala (Engg.) 2002]
Options:
A) $ \frac{d^{2}y}{dx^{2}}+y=0 $
B) $ \frac{d^{2}y}{dx^{2}}-y=0 $
C) $ \frac{dy}{dx}+y=0 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ y=A\sin x+B\cos x $
Therefore $ \frac{dy}{dx}=A\cos x-B\sin x $
Therefore $ \frac{d^{2}y}{dx^{2}}=-A\sin x-B\cos x $
$ =-(A\sin x+B\cos x)=-y $
Therefore $ \frac{d^{2}y}{dx^{2}}+y=0 $ is the required differential equation.
BETA
