Differential Equations Question 173
Question: The solution of $ \frac{d^{2}y}{dx^{2}}={{\sec }^{2}}x+xe^{x} $ is
[DSSE 1985]
Options:
A) $ y=\log (\sec x)+(x-2)e^{x}+c_1x+c_2 $
B) $ y=\log (\sec x)+(x+2)e^{x}+c_1x+c_2 $
C) $ y=\log (\sec x)-(x+2)e^{x}+c_1x+c_2 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{d^{2}y}{dx^{2}}={{\sec }^{2}}x+xe^{x} $
On integrating, $ \frac{dy}{dx}=\tan x+xe^{x}-e^{x}+c_1 $
Again, $ y=\log (\sec x)+xe^{x}-e^{x}-e^{x}+c_1x+c_2 $
Thus required solution is $ y=\log (\sec x)+(x-2)e^{x}+c_1x+c_2 $ .
BETA
