The integrating factor of $\frac{dy}{dx} + \frac{y}{x} = x^3 - 3$ is

If $\frac{dy}{dx} + 2y \tan x = \sin x$,$0 < x < \frac{\pi}{2}$ and $y(\frac{\pi}{3}) = 0$,then the maximum value of $y(x)$ is.

Observe the following statements:
$A$. Integrating factor of $\frac{dy}{dx} + y = x^2$ is $e^x$.
$R$. Integrating factor of $\frac{dy}{dx} + P(x)y = Q(x)$ is $e^{\int P(x) dx}$.
Then, the true statement among the following is:

$y+x^2=\frac{dy}{dx}$ has the solution

Let $y=y(x)$ be the solution curve of the differential equation $\frac{dy}{dx} + \left(\frac{2x^2+11x+13}{x^3+6x^2+11x+6}\right)y = \frac{x+3}{x+1}$,where $x > -1$,which passes through the point $(0,1)$. Then $y(1)$ is equal to:

The general solution of the differential equation $(\sec x + \tan x) \frac{dy}{dx} + (\sec^2 x + \sec x \tan x) y = 1$ is