The integrating factor of the differential equation $x \frac{dy}{dx} - y = x^3, (x > 0)$ is . . . . . . .

If $\frac{dy}{dx} + y \tan x = \sin 2x$ and $y(0) = 1$,then $y(\pi)$ is equal to

If $y = f(x)$ is the solution of the differential equation $\frac{dy}{dx} = (\tan x - y) \sec^2 x$,$x \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right)$,such that $y(0) = 0$,then $y\left( -\frac{\pi}{4} \right)$ is equal to

The integrating factor of the differential equation $(x^2 - 1)\frac{dy}{dx} + 2xy = x$ is

If the solution curve of the differential equation $(2x - 10y^3) dy + y dx = 0$ passes through the points $(0, 1)$ and $(2, \beta)$,then $\beta$ is a root of the equation:

If a curve $y = f(x)$ passes through the point $(1, 2)$ and satisfies $x \frac{dy}{dx} + y = bx^4$,then for what value of $b$ is $\int_{1}^{2} f(x) dx = \frac{62}{5}$?