Differential Equations Question 172
Question: The solution of the differential equation $ {{\cos }^{2}}x\frac{d^{2}y}{dx^{2}}=1 $ is
Options:
A) $ y=\log \cos x+cx $
B) $ y=\log \sec x+c_1x+c_2 $
C) $ y=\log \sec x-c_1x+c_2 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ {{\cos }^{2}}x\frac{d^{2}y}{dx^{2}}=1 $
Therefore $ \frac{d^{2}y}{dx^{2}}={{\sec }^{2}}x $
On integrating, we get $ \frac{dy}{dx}=\tan x\pm c_1 $
Again integrating, we get $ y=\log \sec x\pm c_1x\pm c_2 $ .
BETA
