Which of the following equations is a linear differential equation?

Let $f$ be a differentiable function such that $f'(x) = 7 - \frac{3}{4} \frac{f(x)}{x}$ for $x > 0$ and $f(1) \neq 4$. Then $\lim_{x \to 0^+} x f\left(\frac{1}{x}\right)$

Let $f : (0, \infty) \to (2, 20)$ be a twice differentiable function such that $\lim_{x \to \infty} (f(x) + f'(x) + f''(x)) = \lim_{x \to \infty} g(x)$,where $\lim_{x \to \infty} g(x)$ exists and is equal to $5$. Then $\lim_{x \to \infty} (f(x) - g(x))$ is equal to:

Let $y=y(x)$ be the solution of the differential equation $x \frac{dy}{dx}+y=x \log x, (x > 1)$. If $2(y(2))=\log 4-1$,then the value of $y(e)$ 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:

Let $y=y(x)$ be the solution of the differential equation $x(1-x^{2}) \frac{dy}{dx}+(3x^{2}y-y-4x^{3})=0, x>1$ with $y(2)=-2$. Then $y(3)$ is equal to