For each of the differential equations, find the general solution:
\cfrac{dy}{dx}+2y=\sin\,x
2. \cfrac{dy}{dx}+3y=e^{-2x}
\cfrac{dy}{dx}+\cfrac{y}{x}=x^{2}
4. \cfrac{dy}{dx}+(\sec\,x)y=\tan\,x ...\left(0\le x < \cfrac{\pi}{2}\right)
5. \cos^2x\cfrac{dy}{dx}+y=\tan\,x ...\left(0\le x < \cfrac{\pi}{2}\right)
x\cfrac{dy}{dx}+2y=x^2\log\, x
x\, \log\, x\cfrac{dy}{dx}+y = \cfrac{2}{x} \log x
(1+x^2)dy + 2xy dx = \cot x dx ... (x \neq 0)
x\cfrac{dy}{dx}+y-x+xy\, \cot\, x=0 ...(x\neq 0)
(x+y)\cfrac{dx}{dy}=1
y\, dx+(x-y^2)dy=0
12. (x+3y^2)\cfrac{dy}{dx}=y ...(y > 0)