Let $y$ be the solution of the differential equation with the initial conditions given below. If $y(x=2)=A \ln 2$, then the value of $A$ is _________ (rounded off to 2 decimal places).

$$ x^2 \frac{d^2 y}{d x^2}+3 x \frac{d y}{d x}+y=0 \quad y(x=1)=0 \quad 3 x \frac{d y}{d x}(x=1)=1 $$

If $x(t)$ satisfies the differential equation

$t \frac{dx}{dt} + (t - x) = 0$

subject to the condition $x(1) = 0$, then the value of $x(2)$ is __________ (rounded off to 2 decimal places).

Consider the second-order linear ordinary differential equation

$\rm x^2\frac{d^2y}{dx^2}+x\frac{dy}{dx}-y=0, x\ge1$

with the initial conditions 

$\rm y(x=1)=6, \left.\frac{dy}{dx}\right|_{x=1}=2$

The value of 𝑦 at 𝑥 = 2 equals ________.

(Answer in integer)

For the exact differential equation,

$\frac{du}{dx}=\frac{-xu^2}{2+x^2u}$

which one of the following is the solution?