The integrating factor of $\left(x+2 y^3\right) \frac{d y}{d x}=y^2$ is

Let $x = x(y)$ be the solution of the differential equation $2y^2 \frac{dx}{dy} - 2xy + x^2 = 0, y > 1, x(e) = e$. Then $x(e^2)$ is equal to:

For the primitive integral equation $ydx + y^2dy = xdy$ ; $x \in R$,$y > 0$,$y = y(x)$,$y(1) = 1$,then $y(-3)$ is

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

Let the solution curve $y=y(x)$ of the differential equation $(1+e^{2x})(\frac{dy}{dx}+y)=1$ pass through the point $(0, \frac{\pi}{2})$. Then,$\lim_{x \rightarrow \infty} e^{x} y(x)$ is equal to.

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: