Question

If $\frac{dy}{dx}+y\tan x=sin2x$ and $y\left(0\right)=1$, then $y\left(\pi \right)$ is equal to :

• A. 1
• B. -1
• C. -5
• D. 5

Answer 1

The correct option is C -5

$\frac{dy}{dx}+y\tan x=sin2x$ It is a linear equation

first we find integrating factor

$I.F.=e^{\int \tan xdx}=\sec x$ ................(since integration of $tanx=ln\left(secx\right))$

The general solution is

$y\sec x=\int \sin 2x\sec xdx+C$ ............(simplify $sin2x$ and integrate both sides) .

$\Rightarrow y\sec x=-2\cos x+C$

$\Rightarrow 1=-2+C$

or $C=3$

$y(-1)=2+3$

$\Rightarrow y=-5$