Mathematics - Differential Equation Question with Solution | TestHub

$\frac{dy}{dx}+2\tan x·y=2\sin x$

I.F. $=e^{\int 2\tan xdx}={\sec }^{2}x$

solution is
$y·{\sec }^{2}x=\int 2\sin x·{\sec }^{2}xdx+C$

$y{\sec }^{2}x=2\sec x+C$
$\Rightarrow 0=2.2+C\Rightarrow C=-4$
$y{\sec }^{2}x=2\sec x-4$
$y\left(\frac{\pi }{4}\right)=\sqrt{2}-2$