The solution of the differential equation $2x \frac{dy}{dx} - y = 3$ represents a family of

Let $f:[1, \infty) \rightarrow[2, \infty)$ be a differentiable function. If $10 \int_1^{x} f(t) dt = 5x f(x) - x^5 - 9$ for all $x \geq 1$,then the value of $f(3)$ is:

Let $y=y(x)$ be the solution curve of the differential equation $(1+x^{2})dy+(y-\tan^{-1}x)dx=0$, with $y(0)=1$. Then the value of $y(1)$ is:

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

The integrating factor of the differential equation $\frac{dy}{dx} + \frac{1}{x}y = x^3 - 3$ is

If $y = y(x)$ is the solution of the differential equation $\sqrt{4-x^2} \frac{dy}{dx} = \left(\left(\sin^{-1}\left(\frac{x}{2}\right)\right)^2 - y\right) \sin^{-1}\left(\frac{x}{2}\right)$ for $-2 \leq x \leq 2$ with $y(2) = \frac{\pi^2-8}{4}$,then $y^2(0)$ is equal to