Differential Equations Question 109
Question: The differential equation whose solution is $ y=c_1\cos ax+c_2\sin ax $ is (Where $ c_1,\ c_2 $ are arbitrary constants)
[MP PET 1996]
Options:
A) $ \frac{d^{2}y}{dx^{2}}+y^{2}=0 $
B) $ \frac{d^{2}y}{dx^{2}}+a^{2}y=0 $
C) $ \frac{d^{2}y}{dx^{2}}+ay^{2}=0 $
D) $ \frac{d^{2}y}{dx^{2}}-a^{2}y=0 $
Show Answer
Answer:
Correct Answer: B
Solution:
Solution is $ y=c_1\cos ax+c_2\sin ax $
Differentiate it w.r.t. x, we get $ \frac{dy}{dx}=-c_1a\sin ax+c_2a\cos ax $
Again $ \frac{d^{2}y}{dx^{2}}=-c_1a^{2}\cos ax-c_2a^{2}\sin ax $
$ \frac{d^{2}y}{dx^{2}}=-a^{2}(c_1\cos ax+c_2\sin ax)\Rightarrow \frac{d^{2}y}{dx^{2}}=-a^{2}y $
or $ \frac{d^{2}y}{dx^{2}}+a^{2}y=0 $ .
BETA
