A) \[2+\frac{1}{e}\]
B) \[\frac{1}{2}-e\]
C) \[e-2\]
D) \[\frac{1}{2}-e\]
Correct Answer: C
Solution :
\[\frac{dy}{dx}=(tan\,x-y)se{{c}^{2}}x\] Now, \[put\,\tan x=t\Rightarrow \frac{dt}{dx}=se{{c}^{2}}x\] So\[\frac{dy}{dt}+y=t\] On solving, we get \[y{{e}^{t}}={{e}^{t}}(t-1)+c\] \[\Rightarrow y=(tanx-1)+c{{e}^{-\tan x}}\] \[\Rightarrow y(0)=0\Rightarrow c=1\] \[\Rightarrow y=\tan x-1+{{e}^{-\tan x}}\] So \[y\left( -\frac{\pi }{4} \right)=e-2\]You need to login to perform this action.
You will be redirected in
3 sec