Solution of Linear Differential Equations

If $y+\frac{d}{dx}\left(xy\right)=x(\sin x+\log x)$ then

The solution of differential equation $\frac{dy}{dx}-y\tan x=-y^2\sec x$ is

The integrating factor of the differential equation $\frac{dy}{dx}\left(x\ln x\right)+y=2\ln x$ is given by

The solution of the differential equation $\frac{dy}{dx}+\frac{2yx}{1+x^2}=\frac{1}{{\left(1+x^2\right)}^2}$ is

Equation of a curve which satisfies the differential equation $\frac{dy}{dx}=\frac{y^2-6y+9}{6x-2xy-1}$ and passes through the point $\left(1,2\right)$ will be

Solution of the differential equation $\frac{dy}{dx}+\frac{y}{x}=\sin x$ is