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. $=e^{\int \tan xdx}=e^{\log \sec x}=\sec x$
$y.secx=\int \sin 2x\cdot \sec xdx+c$
$=\int 2\sin x\cdot \cos x\cdot \sec xdx+c$
$y\sec x=-2\cos x+c$
$y(0)=11.1=-1.2+c$
$\Rightarrow c=3$
$y\sec x=-2\cos x+3$
$y(\pi )=$ ? $y(-1)=(-2)(-1)+3$
$\Rightarrow -y=5$
$\Rightarrow y=-5$