Integrating factor of $x \frac{dy}{dx} - y = x^4 - 3x$ is

Let $y=y(x)$ be a solution curve of the differential equation $(y+1) \tan ^{2} x \,dx+\tan x \,dy+y \,dx=0$ for $x \in \left(0, \frac{\pi}{2}\right)$. If $\lim _{x \rightarrow 0+} x y(x)=1$,then the value of $y\left(\frac{\pi}{4}\right)$ is:

The solution of the differential equation $y' = y \tan x - 2 \sin x$ is

The solution of the differential equation $x\frac{dy}{dx} + y = x^2 + 3x + 2$ is

The solution of the differential equation,$(x + 2y^3) \frac{dy}{dx} = y$ is :

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