Question

If $\frac{dy}{dx}+y$ tan x = sin 2x and y(0) = 1, then y$\left(\pi\right)$ is equal to :

• A. 1
• B. -1
• C. -5
• D. 5

Answer 1

Answer: (C)

I.F. $= e ^{\int \tan\, x dx }= e ^{\log \,\sec\, x}=\sec \,x $
$y. sec \, x=\int \sin \,2 x \cdot \sec\, x \,dx+c $
$=\int 2\, \sin x \cdot \cos \,x \cdot \sec\, x \,dx+c $
$y \,\sec \,x=-2 \,\cos\, x+c $
$y(0)=1 \,\, 1.1=-1.2+ c$
$ \Rightarrow \,c =3 $
$y\, \sec\, x=-2 \cos \,x+3 $
$y(\pi)=$ ? $y(-1)=(-2)(-1)+3$
$\Rightarrow -y=5$
$ \Rightarrow y=-5$