Which one of the following is a linear differential equation?

For a differentiable function $f: \mathbb{R} \rightarrow \mathbb{R}$,suppose $f^{\prime}(x)=3 f(x)+\alpha$,where $\alpha \in \mathbb{R}, f(0)=1$ and $\lim _{x \rightarrow-\infty} f(x)=7$. Then $9 f\left(-\log _{e} 3\right)$ is equal to ............

Let $f: R \to R$ be such that $f(xy) = f(x)f(y)$ for all $x, y \in R$ and $f(0) \ne 0$. Let $g: [1, \infty) \to R$ be a differentiable function such that $x^2 g(x) = \int_1^x (t^2 f(t) - t g(t)) dt$. Then $g(2)$ is equal to:

Find the general solution of the differential equation:
$\frac{dy}{dx} + (\sec x)y = \tan x$,where $0 \le x \le \frac{\pi}{2}$.

The particular solution of $e^{\frac{y}{x}} = x, y(1) = 3, x > 0$ is . . . . . . .

Let $x=x(y)$ be the solution of the differential equation $2 y e^{x / y^{2}} d x+\left(y^{2}-4 x e^{x / y^{2}}\right) d y=0$ such that $x(1)=0$. Then,$x(e)$ is equal to